Using a cut of meat without too much connective tissue will definitely help.
Talk to your butcher about good options.
Stew meat isn't the best choice; it contains a lot of connective tissue which breaks down during the long, slow stewing process.
Grilling is too hot and quick to break down that tissue.
If you do grill stew meat, lower temperature and longer cooking time may help some, but in that case you'll probably want to do the veggies separately.
A good marinade will help.
You can add some meat tenderizer, or make fresh pineapple juice one of the marinade ingredients.
Pineapple contains an enzyme that'll break down some of the connective tissue, but it has to be fresh -- canned juice will have been heated, destroying the enzyme.
cooking.stackexchange.com/users/5505/Caleb
Also, they aren't as pretty with this strategy, but I've begun skewering my shish kabobs more in line with cooking time than for aesthetics.
So I will skewer all my meat together...
This would allow you to cook your meat kabobs seperately and only until they are cooked rather than trying to get everything on the kabob to cook at the right time.
Admittedly, I know once you get really good at this, it's totally doable (to cook it all on the same skewer), but I'm not there, and it might make your life easier as well...
cooking.stackexchange.com/users/6791/Rikon
a proper marinade helps, but if you want juicy soft meat there is no substitute for fat .
The meat must have marbling and not come from an old animal.
Also, scoring the meat before marinading helps the liquid penetrate.
tenderizing chemicals like pinapple juice or papaya do work, but they can leave you with a mushy texture - not very appetizing.
Experiment before you get a nickname and a place in the family history...
cooking.stackexchange.com/users/4558/Walter A. Aprile
I have found a pin style meat tenderizer (before you cube or marinade the meat) to be very helpful in using a cuts that might otherwise prove "too chewy".
This model is on Amazon .
Once penetrated by this type of tenderizer a good marinade (BEER) will work wonders on those connective tissues.
cooking.stackexchange.com/users/6279/Cos Callis
Another option is to cook the meat low and slow.
Once the meat is tender, let it cool in the fridge.
Once it's cooled, you can skewer it on to the shish (or is it the kabob?).
The high heat will now caramelize the outside and warm the inside.
At least in theory.
cooking.stackexchange.com/users/641/BaffledCook
try marinating stewing beef in your favorite marinade...then sprinkle some coffee grounds into it.
mix thouroughly.
i did this last week...
marinated in the fridge for a day.
the tough cut was sooooo tender and cooked quickly with the veggies.
i sliced the stew beef in at least half to get quarter inch thick pieces.
my buddy was amazed....
as was i.
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I know I'm coming late to this discussion, but thought I'd answer for those referencing or googling the topic!
I use stew beef for souvlaki and shish kabob all the time.
The 2 best ways to get it tender are: 1)
Marinate over night in yogurt, just google yogurt marinades, but make sure you are using plain Balkan style yogurt 2) brine.
This is my favourite because it's more adaptable.
Brining is not just for poultry or pork.
Just google brine for beef, but this is the ratio I start with 2 3/4 cups water1/4 cup salt3 tablespoons brown sugar2 cups ice Bring water salt and sugar to a low boil to dissolve sugar and salt.
Do not lower amounts of salt or sugar.
These are what break down the meat fibres and make it tender.
The meat will not be salty.
Add 2 cups of ice and let cool completely.
Place meat and brine in a baggie and keep in the fridge for a minimum of 2 hours, but preferably overnight.
Rinse the meat.
Pat dry.
Put on skewers with whatever accoutrement you like and grill away.
That is a basic brine.
I like to add extra stuff depending on my mood.
During the boiling stage I'll add things like mustard, herbs, vanilla and/or liquid smoke.
Many have mentioned beer.
Instead of ice, add alcohol during cooling stage.
I like adding Guinness.
Other faves are whiskey/bourbon or a bold red wine like Shiraz.
Do not add alcohol during boiling stage ( particularly whisky), as it will flare up.
Hope this helps!!
Ps-
if I'm adding a BBQ sauce ( I rarely do)
I only add it in last few minutes of grilling, and I try to use something similar to the brine.
Guinness BBQ Sauce if I had Guinness in the brine for example.
Pps.
Also makes a difference to whole kabob if you Marinate the veggies.
Just use a cheap store brand Italian salad dressing.
Place pre cut veggies and dressing in a baggie and Marinate for as long as you like.
cooking.stackexchange.com/users/48240/Lori
We cut beef stew into one inch cubes and pierce them on a stick with cherry tomatoes, onions, green peppers, etc, and grill them nicely.  The meat is brown and grilled on the outside, pinkish in the middle, vegetables are grilled, but the meat ends up being not so tender.  How can I make the Shish Kabobs tender?
How do you grill Shish Kabobs so they aren't so chewy?
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cooking.stackexchange.com/users/7000/LarsTech
Talk to your butcher about good options with fat but not much connective tissue as in stewing beef. Marinading and tenderising the meat can be helpful, as can cooking low and slow. Local for a better cut of meat for this. You can also try marinading it or tenderizing it before cooking.
Talk to your local butcher about meat cuts that are more appropriate for this. A good marinade will help make the meat more tender. Tenderize the meat first. Cook the meat separately on a low heat until tender.