In this paper some elements of the theory of fractal labyrinths are presented using fractional calculus mathematics and random walk model. A model of finitely ramified deter- ministic labyrinth fractal on a square grid is built, topology of its boundaries is defined, its pathways are calculated using the path matrices up to isomorphism accuracy with respect to rotation and flipping. The path matrices were calculated using the Jordan decomposition. For the constructed model of a fractal labyrinth there have been obtained numerical values of the labyrinth path’s lengths before its exits, allowing obtaining the characteristics of the simulated fractal environment.