The recent use of anti-angiogenesis (AA) drugs for the treatment of glioblastoma multiforme (GBM) has uncovered unusual tumor responses. Here, we derive a new mathematical model that takes into account the ability of proliferative cells to become invasive under hypoxic conditions; model simulations generate the multilayer structure of GBM, namely proliferation, brain invasion, and necrosis. The model is able to replicate and justify the clinical observation of rebound growth when AA therapy is discontinued in some patients. The model is interrogated to derive fundamental insights int cancer biology and on the clinical and biological effects of AA drugs. Invasive cells promote tumor growth, which in the long run exceeds the effects of angiogenesis alone. Furthermore, AA drugs increase the fraction of invasive cells in the tumor, which explain progression by fluid-attenuated inversion recovery (FLAIR) signal and the rebound tumor growth when AA is discontinued.