Cubic symmetric Mass-Spring Systems (MSS) for simulating isotropic elastic materials are known to be intrinsically limited by the Cauchy constraints (rari-constant theory) involving Poisson ratio of exactly ν = 1/4. To mitigate the impact of this restriction, we propose a new solution based on correction forces, which authorizes to use MSS for materials with ν ∈]0; 0.5[. The validation of our model is evaluated by comparing its response to various deformations with Finite Element Model (FEM). The results show that the proposed model is relevant to simulate any compressible isotropic elastic material, and in particular nearly incompressible (Poisson ratio ≃ 0.5) biological soft tissues for which it is dedicated.