Jordon Saxton, from Faringdon, Oxfordshire, was convicted of the manslaughter of 11-week-old Jayden Saxton, but cleared of his murder.
Jayden died in November after suffering 18 bone fractures as well as multiple brain and spinal injuries, a trial at Oxford Crown Court heard.
Saxton, 21, was sentenced to nine years in prison.
During the two-week trial, jurors heard the baby was living at a flat with his parents and had been left alone with Saxton on 17 November.
They heard that Jayden never recovered from what the prosecution described as a "violent assault", in which he was squeezed so hard several of his ribs were broken.
He was taken to hospital by paramedics, but died the following day.
During the trial, Saxton told the court he had dialled 999 after Jayden stopped breathing and was in a state of panic because he thought something was stuck in his son's throat.
Passing sentence, Mr Justice Rabinder Singh QC, said the baby's death was "undoubtedly a tragedy for everyone concerned".
He told Saxton: "No-one but you will ever know exactly what happened that afternoon.
"I conclude that you acted as you did in frustration at the fact that you could not settle Jayden."
Det Ch Insp Kevin Brown of Thames Valley Police said Jayden's family had been through a "living nightmare" since November.
"The medical and forensic evidence in this investigation proved how Jayden was assaulted, causing him serious bodily harm that led to his death.
"The evidence was clear that Jordan committed manslaughter."
Adrian Foster, chief prosecutor for Thames and Chiltern Crown Prosecution Service (CPS) said it was "impossible to imagine a more vulnerable victim".
He said that old rib fractures also discovered during the post mortem indicated that Jayden had previously been forcibly gripped and shaken between 21 October and 4 November.
"Jordan Saxton denied causing the death of his defenceless son and offered no explanation for how he obtained his injuries," he added.

The development was announced by First Minister Nicola Sturgeon during a visit to the yard on Monday.
She said the contract would create new jobs at Ferguson and secure employment for the existing 150-strong workforce.
The yard went bust a year ago, but was taken over by entrepreneur Jim McColl who plans to invest up to £65m.
The deal, when finalised, will see the Ferguson yard build two vessels for the Caledonian Maritime Assets Ltd's (CMAL) fleet.
Ms Sturgeon said: "This is an excellent result for Ferguson Marine Engineering Limited and I am delighted to name them as preferred tenderer for the contract to build two new ferries, the largest commercial vessels to be built on the Clyde since 2001.
"This contract will see the 150-strong workforce retained and more staff taken on at the shipyard, underlining our commitment to creating the vital jobs needed to boost local economies and help stimulate growth across Scotland.
"The Scottish government is committed to supporting ferry users around Scotland by providing safe and reliable services, and this is the latest step to ensuring we have a fleet that continues to deliver for the communities that depend on it."

Japanese exports rose by just 0.6% in September from a year earlier, much slower than in previous months.
The data is seen as reflecting a slowdown in Japan's top trading partner, China.
However, the Nikkei 225 closed 1.9% higher at 18,554.28 on hopes the weak data would trigger more stimulus efforts from the government.
In China, the mainland's benchmark Shanghai Composite closed down 3.06% at 3,320.68.
Hong Kong's Hang Seng remained closed on Wednesday for a public holiday.
In Australia, the S&P/ASX 200 rose by 0.2%, closing at 5,248.30.
Shares in mining giant BHP Billiton rose 1% after it maintained its full-year production guidance for iron ore.
Slowing growth in China has been weighing on mining stocks in recent weeks as the country is the main importer of Australian commodities.
South Korea's benchmark Kospi index rose marginally by 0.2% to finish at 2,042.98.
Shares of LG Electronics jumped by more than 14%, boosted by a fresh supply agreement with General Motors.
A man has been jailed for killing his baby son after squeezing his chest and shaking him.
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The Ferguson Marine shipyard in Port Glasgow has been named as the preferred bidder for a £97m contract to build two ferries to operate in Scotland.
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Japanese shares rose on Wednesday, despite news of disappointing export growth last month.