This paper explores the modelling capacities of a new class of P systems, called kernel P systems (kP systems). A specific language for describing kP systems and its translation into Promela, the specification language of Spin, are described. This Promela specification has been further used for simulation and property verification with the Spin model checker. Also, a parallel implementation on GPU parallel architectures, realized using CUDA, is presented and the results are compared with the ones obtained using Promela and Spin. A case study, namely the Subset sum problem, which has been modelled with kernel P systems and further implemented in Promela is presented.