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This master´s thesis deals with processing and analysis of data, acquired from experimental examination performed with functional magnetic resonance imaging technique. It is an oddball type experimental task and its goal is an examination of cognitive functions of the subject. The principles of functional magnetic resonance imaging, possibilities of experimental design, processing of acquired data, modeling of a response of organism and statistical analysis are described in this work. Furthermore, particular parts of preprocessing and analysis are carried out using real data set from experiment. The main goal of this work is suggestion and realization of model, which enables advanced categorization of stimuli, considering the type of previous rare stimulus and the number of frequent stimuli within them. With its in-depth categorization, this model enables detail exploration of cerebral processes, associated mainly with attention, memory, expectancy or cognitive closure. The second point of that work is an evaluation of models of hemodynamic response, which are applied in statistical analysis of data from fMRI experiment. Comparison of basis functions, the models of hemodynamic response to experimental stimulation used for general linear model, is performed in this work. The result of this comparison is an evaluation of detection efficiency of activated voxels, false positivity rate and computational and user difficulty.