In this paper we present some of our work on approaches of generating simulation code from equation-based mathematical models that can be executed on parallel architectures, especially CUDA-enabled GPUs. The models are written in the objectoriented equation-based language Modelica. We show that it is possible to automatically generate simulation code for purecontinuous-time models that can be reduced to an ordinary differential equation system without algebraic loops and where the initial values of all variables and parameters are known at compile time. Implementation work has been carried out in the OpenModelica compiler (an open source implementation of a Modelica compiler). In this paper we discuss previous, ongoing, and potentially future work