In this paper, we present the simulation of an abstract model of SIMD type with vertical data processing (the STAR-machine) on GPU with CUDA framework. There is a number of algorithms developed for the STAR-machine. The research conducted recently shows that such a model is extremely efficient when used to solve graph problems. Associative operations are the key properties of this model. In particular, all of them take constant time. In this paper, we present an implementation of associative operations on GPU (Graphic Processing Units). This study is aimed at providing a bridge or a general manual instruction to convert the STAR algorithms to the GPU implementation. As the architecture of the STAR-machine in modern technologies has not been built yet, this provides a possible way to implement the STAR algorithms on an alternative platform to verify their correctness and efficiency, especially, for massive data input.