The demand for running complex applications on smart mobile devices is rapidly increasing. However, the limitations of resources are restricting the development of intensive applications on these devices. The restrictions can be overcome by offloading the computation of an application in the powerful cloud servers. The objective of the computation offloading is to offload the parts of an application to the cloud server to minimize the response time, energy consumption and monetary cost of the application. Unlike prior work in computation offloading, this work considers the effect of parallel execution—on different devices (external parallelism) and on the different cores of a single device (internal parallelism). This work models each device as a multi-server queueing station. It uses genetic algorithm to determine the near-optimal offloading allocation. The results show that considering the effect of parallel execution yields better pareto-optimal solution for the allocation problem compared to excluding parallelism.