The council has cited "unprecedented cuts in government funding" and rising levels of demand for services by the over-65s and children's sectors.
Since 2011 the council has axed some 600 roles.
The proposals will be considered at a committee meeting on 18 July. The council said there could be even further cuts because of Brexit.
Labour council leader Jo Lovelock said: "Whilst no-one can know for sure what the effect of the recent EU vote will be, further cuts in local government funding are possible.
"We do know that over the next four years the government will further reduce the revenue support grant income Reading receives by 92%.
"Unfortunately, savings proposals such as these are a direct consequence."
Losing 200 members of staff - not including teachers and other employees who work in education - would mean a 10% reduction in the council's 2,000-strong workforce.
Ms Lovelock said: "Things are going to take longer, some things won't happen at all and people will notice that the council can't be as proactive as it has been."
About £5.9m is planned to go from children's, education and early help services.
The council will need to save about £36.7m by 2020 due to a funding gap from central government.
Ms Lovelock added: "These are the latest in a long line of savings we are having to consider following the unprecedented cuts in government funding.
"We have a legal duty to deliver a balanced budget."
The council says the population has increased to 159,200 - about 9% - since 2001 and there has been an increase of so-called heavy service users like the over-65s and children.
The cuts were announced at a meeting on Friday, where the council also released proposals to "save all libraries" from closure by reducing their opening hours.
Weekly opening hours at the eight libraries will be reduced by between five and 15 hours.
Some, including Whitley and Southcote libraries, could be moved to neighbouring community centres in a measure that could save about £290,000.
About 200 jobs could go at Reading Borough Council as the authority makes plans to save nearly £20m.