Brain computer interface (BCI) is a new communication way between man and machine. It identifies mental task patterns stored in electroencephalogram (EEG). So, it extracts brain electrical activities recorded by EEG and transforms them machine control commands. The main goal of BCI is to make available assistive environmental devices for paralyzed people such as computers and makes their life easier. This study deals with feature extraction and mental task pattern recognition on 2-D cursor control from EEG as offline analysis approach. The hemispherical power density changes are computed and compared on alpha-beta frequency bands with only mental imagination of cursor movements. First of all, power spectral density (PSD) features of EEG signals are extracted and high dimensional data reduced by principle component analysis (PCA) and independent component analysis (ICA) which are statistical algorithms. In the last stage, all features are classified with two types of support vector machine (SVM) which are linear and least squares (LS-SVM) and three different artificial neural network (ANN) structures which are learning vector quantization (LVQ), multilayer neural network (MLNN) and probabilistic neural network (PNN) and mental task patterns are successfully identified via k-fold cross validation technique.