More than 32,000 soldiers failed a basic fitness test at some point in the past three years, and more than 22,000 were found to be overweight and at risk of health problems, according to Ministry of Defence figures.
All soldiers in the British army are required to complete a personal fitness assessment twice a year, and those who fail must retake the test within seven days. Multiple failures could result in being discharged.
Men under the age of 29 must complete 44 press-ups in two minutes, followed by 50 sit-ups in two minutes, and a 1.5-mile (2.4-kilometre) run within 10.5 minutes.
Women have a slightly easier test, with 21 press-ups, 50 sit-ups and 13 minutes in which to complete the run, while the rules are relaxed for older soldiers.
According to the figures obtained by the Sunday Times newspaper, 29,600 men and 2,819 women failed their fitness tests between April 2011 and March 2014.
"This figure represents 11 percent of the army serving in that period and many of those who failed will have subsequently passed their fitness test," the Ministry of Defence said in a statement.
"All personnel are provided with the support and training necessary to meet the army's physical standards, with additional help for those personnel who fail to meet this criteria.
"Personnel who remain unable to meet the standard could ultimately be discharged."
The Sunday Times also revealed that more than 22,000 troops were found to be at increased risk of type 2 diabetes, high blood pressure and heart disease because they were so unfit.
In a story headlined "Too fat to fight," the newspaper quoted one senior officer who blamed the "appalling diet" of many troops.
"While soldiers can have salads and low-calorie meals, they can also have a cooked breakfast, followed by chips at lunch and chips at dinner and a stodgy pudding, too," the officer said.
The figures on fitness do not include those injured in Iraq and Afghanistan or those recovering from illness or training injuries, the newspaper said.