An application development and verification method for massively parallel systems using NVIDIA GPUs is proposed. The method allows creating models at different levels of abstraction using the apparatus of marked transition systems. The compositions (product) of such systems are transformed into a Petri net, which are then analyzed by appropriate means. The proposed method allows specifying model properties by temporal logic formulas. This allows studying the properties of massively parallel systems which is almost impossible to analyze manually, since the number of execution threads in the latest NVIDIA video adapter architectures (Pascal, Volta, Turing, Ampere) is measured in hundreds of thousands or millions.