As the development of high-performance computing (HPC) is growing, exascale computing is on the horizon. Therefore, it is imperative to develop parallel systems, such as graphics processing units (GPUs) and programming models, that can effectively utilise the powerful processing resources of exascale computing. A tri-level programming model comprising message passing interface (MPI), compute unified device architecture (CUDA), and open multi-processing (OpenMP) models may significantly enhance the parallelism, performance, productivity, and programmability of the heterogeneous architecture. However, the use of multiple programming models often leads to unexpected errors and behaviours during run-time. It is also difficult to detect such errors in high-level parallel programming languages. Therefore, this present study proposes a parallel hybrid testing tool that employs both static and dynamic testing techniques to address this issue. The proposed tool was designed to identify the run-time errors of C++ and MPI + OpenMP + CUDA systems by analysing the source code during run-time, thereby optimising the testing process and ensuring comprehensive error detection. The proposed tool was able to identify and categorise the run-time errors of tri-level programming models. This highlights the need for a parallel testing tool that is specifically designed for tri-level MPI + OpenMP + CUDA programming models. As contemporary parallel testing tools cannot, at present, be used to test software applications produced using tri-level MPI + OpenMP + CUDA programming models, this present study proposes the architecture of a parallel testing tool to detect run-time errors in tri-level MPI + OpenMP + CUDA programming models.