In the last decades several highly efficient linear algebra systems have been developed, which became an essential part in scientific computing. Only minor attention has been spend on the numerical evaluation and the solution of piecewise linear systems. In this paper, we address this problem and focus on the efficient evaluation of piecewise linear functions in Abs-Normal Form (ANF). Therefore, four different methods are presented that partly exploit parallelism. For all methods, we discuss their theoretical limitations and give details for an efficient implementation on GPUs using CUDA. We also provide some approximations for the expected run-time in case of general dense ANFs. The theoretical results are compared with real run-time experiments. We expect that this discussion provides valuable insights about the capabilities of the proposed approaches and will help to design highly efficient extensions of (cu-)BLAS for piecewise linear functions.