We consider Yip's formulation of the Ericksen model for an elastic bar on an elastic foundation [63] which leads to the Euler-Lagrange equation for the functional Îµ(u) = â« between 0 and 1 (Î³uÂ²xx +W(ux) + ÉuÂ²)dx, where x is an element of the set (0, 1). with double Dirichlet boundary conditions. Here the potential W(p) = ((|p| - 1)Â²), is not differentiable at p = 0.We define and prove existence and uniqueness of periodic solutions with any number n â¥ 0 of internal zeroes for all É, Î³ > 0 and discuss the existence of non-periodic solutions.The Euler-Lagrange equation contains conditions that make it diffcult to track, and then dropping one of them we obtain a weak formulation for this reduced problem,which we then prove it has a unique solution. Next, we use a combination of two numerical methods, namely the Finite Elements Method (FEM) to approximate the model and the Derivative Free Optimization (DFO) to find the location of the jump.