We can find classification problem in many different types of scientific areas and because of that in the last couple of decades there is a lot of proposed procedures which should be able to solve this problem. Facial emotion recognition is one of the problems that can be solved by designing classification model. Classification models have ability to join predefined class labels to each sample contained inside input dataset. In this paper, radial basis function network is used as classifier and results show that this type of classifier is able to successfully solve classification problem. For classification model to be made, it is necessary to define dataset which contains relevant information for solving a given problem. To build classifier with ability to solve facial emotion recognition problem FER2013 dataset was used and experiment results shown that it is possible to build reliable classification model with this dataset. Problem with this dataset is data representation. Data is represented by images and classification algorithms can not work with that type of input. Because of that, feature extraction procedure is carried out on input dataset where essential information is extracted from images. Extracted data then can be used by classification algorithms as input. In this paper three algorithms for feature extraction were described - HOG, LDA and LDA. Experiment results show that models trained on dataset whose features were extracted with LDA algorithm gave best results. Model quality is also influenced by classification algorithm that is used for training. Experiment results show that PSO algorithm gives better results then random algorithm and K-means algorithm. Beside radial basis function network there are other types of classifiers that can be used for solving classification problems e.g. random forest algorithm and support vector machines. Also, it is experimentally determined that radial neural network achieves better performance in comparison to several other classifiers from literature, which makes it a suitable classifier for this problem.