Tumoral angiogenesis and anti-angiogenesis are modeled as a Nash game. We consider the vessel-matrix-tumor system as a porous medium from the tumor viewpoint and as an elastic structural medium from the host tissue viewpoint. We define a competition between two density functions which are intended to represent respectively activators and inhibitors of angiogenesis. The activators want to minimize the pressure drop while the inhibitors intend to minimize the elastic compliance of the matrix or the drainage of the tumoral neovascularization. Numerical results illustrate how -theoretical- tumors develop multiple channels as an optimal response to optimal distribution of inhibitors.