The simulation of granular flows such as landslides or snow avalanches can be modeled using the shallow water equations and appropriate models for the friction terms. However, standard shallow water models assume a constant vertical velocity over the height of the water. In this talk, I will present a recently developed model that allows for velocity profiles that vary with height. This enables the simulation of more realistic application cases. I will discuss properties of the model and present detailed results on the hyperbolicity loss of the model. This loss of hyperbolicity can lead to numerical instabilities and results in an ill-posed system. I will show several possibilities to obtain a hyperbolic system by a systematic simplification of the model. The improved model shows good accuracy and convergence in numerical tests.