Question: I was on about 87 kg to 88 kg. With my height of 1,94 m, it was pretty damn good in terms of my BMI :) I nearly hit exactly the middle of the target value of a mid-twenty male. 
However, I started to train for a run a few weeks ago. I'm running nearly every second day (8 to 11 km) and do a few push-ups (20) and sit-ups (30) twice per day. 

I noticed that I've gained about 3 kg! Okay, I just would've thought "Yep, have to be the additional muscles" but it concerns me, that my BMI is out of range. Is the BMI reliable when it comes to added muscle mass? Should I try to stay in the target range regardless of the training?

Answer: 
No, do not use BMI to gauge your fitness level.

First of all, and I love pointing this out; the person who invented the BMI scale said that it should NOT be used to indicate the level of fatness in a person.

Second of all, it was invented between 1830 and 1850. Our knowledge of the human body has evolved so much now, that it's a marvel that it's still being used.

BMI categories are generally regarded as a tool for measuring whether sedentary individuals are underweight, overweight or obese with **various exceptions**, such as: athletes, children, the elderly, and the infirm.

Look at that list of exceptions.

The term "athletes" in this regard is really anyone who actively works out.

Sources and extra reading:

* Adolphe Quetelet — The Average Man and Indices of Obesity
* [Commentary: Origins and evolution of body mass index (BMI): continuing saga](http://ije.oxfordjournals.org/content/early/2014/03/29/ije.dyu061.full)
The respondanse have been correct, B.M.I is a flawed way of measuring fat to bone/muscle. Hip to waist measurements provide far a better idea of how much fat you carry. More sophisticated techniques give accurate measurements but are costly.
What to do??? Not always easy to do, but simple to quantify, use more calories in exercise than consumed by mouth will ALWAYS do the job. A more simple take home message " Don't eat it if it takes too much effort to burn off"
David W Cornwall