Glioma is a highly invasive form of brain tumor. We have studied the invasion process in a in vitro experiment where tumor spheroids are seeded in collagen gels. We find that invasion involves strong and complex interactions with the gel; the cells deform and align the matrix. In order to better understand this process we study a micromechanical model of collagen-I. We can reproduce the non-linear elasticity of the gel, and we show that deformations are non-affine. We discuss the relationship of the mechanics to the invasive process.