In this study we propose a method using multi layer perceptron (MLP) neural networks to evaluate and predict the performance of parallel systems and report our findings. Artificial neural networks may provide a good alternative to conventional methods in terms of identifying the contribution of individual system and application parameters to performance. Neural network models presented here are used to predict the computational and communication performance of parallel applications running on different platforms. Two applications are considered: the first one is a 2-Dimensional Fast Fourier Transform (FFT) application that requires intensive data exchange between processors, which is valuable for communication performance tests and the second one is a Monte Carlo application which can be classified as a typical floating-point application. There are two types of data used to train, validate and test the neural network models. A large portion of the input data composed from real measurements taken on SunSparc workstations. To enhance the available data, results obtained by modeling some unavailable systems into PACE (the Performance Analysis and Characterization Environment) have been also included.