With the rapid development of smart mobile devices, mobile applications are becoming more and more popular. Since mobile devices usually have constrained computing capacity, computation offloading to mobile edge computing (MEC) to achieve a lower latency is a promising paradigm. In this paper, we focus on the optimal offloading problem for streaming applications in MEC. We present solutions to find offloading policies of streaming applications to achieve an optimal latency. Streaming applications are modeled with synchronous data flow graphs. Two architecture assumptions are considered — with sufficient processors on both the local device and the MEC server, and with a limited number of processors on both sides. The problem is generally NP-complete. We present an exact algorithm and a heuristic algorithm for the former architecture assumption and a heuristic method for the latter. We carry out our experiments on a practical application and thousands of synthetic graphs to comprehensively evaluate our methods. The experimental results show that our methods are effective and computationally efficient.