The paper argues that, the third generation of neural networks – the spiking neural networks (SNN), can be used to model dynamic, spatio-temporal, cognitive brain processes measured as functional magnetic resonance imaging (fMRI) data. The paper proposes a novel method based on the NeuCube SNN architecture for which the following new algorithms are introduced: fMRI data encoding into spike sequences; deep unsupervised learning of fMRI data in a 3D SNN reservoir; classification of cognitive states; connectivity visualization and analysis for the purpose of understanding cognitive dynamics. The method is illustrated on two case studies of cognitive data modelling from a benchmark fMRI data set of seeing a picture versus reading a sentence.