Based on internal constraints depending on the deformations, an initially compressible solid can be mathematically prescribed to become less compressible during the motion and tends to become incompressible for larger deformations. This behavior is defined within this work as limited compressibility. Physically and geometrically non-linear constitutive equations for limited compressible elastic solids are derived, both for Cauchy and Green elasticity, which leads to an extension of the material equations for incompressible elastic solids such as Mooney-Rivlin or Neo-Hookean materials. The material response to the uniaxial extension state of a limited compressible elastic solid is analytically calculated as an example. By using the test results of an uniaxial extension for rubber, it is shown that the derived constitutive equations are able to simulate the measured values and deliver acceptable results.