The paper proposes methods and algorithms for collision detection of bounding cylinders that surround the geometry of virtual objects. The proposed solutions are based on the separating axis theorem and analysis of possible contact interaction cases between two cylinders. The idea is to approximate the cylinders by prisms with their Gauss map to the unit sphere, which reduces the number of separating axes. Also, to compute contact points, an approach was developed based on fast geometric tests, in which polygon and segment are clipping by a prism, as a common perpendicular between line segments and a point on the circle are found. Based on methods and algorithms proposed in this work, software modules were implemented. Approbation of these modules in the virtual environment system VirSim, which was developed in Scientific Research Institute for System Analysis of the Russian Academy of Sciences, showed the adequacy and effectiveness of created methods and algorithms for real-time simulation of virtual cylindrical objects. The results obtained in this work can be used to solve many practical problems in virtual environment systems, training complexes, educational applications, animation, computer games, etc.