[en] A method is developed to find physically valid analytic solutions to the Einstein field equations for a static, spherically symmetric distribution of matter. A generating function can be chosen such that it satisfies physical constraints, and the metric is obtained by quadratures. Three physically valid solutions (i.e., infinity>μ>p>0, p'>0, dp/dμ<1 within the distribution of matter, where μ and p are the density and pressure, respectively) are given as examples. For one of these solutions it is shown that Schwarzschild's interior solution may be obtained as a special case, but only for a specific choice of a parameter which is prohibited by the physical constraints