MPI is widely used as the bedrock of HPC applications, but there are no effective systematic software testing techniques for MPI programs. In this paper we develop COMPI, the first practical concolic testing tool for MPI applications. COMPI tackles two major challenges. First, it provides an automated testing tool for MPI programs – it performs concolic execution on a single process and records branch coverage across all. Infusing MPI semantics such as MPI rank and MPI_COMM_WORLD into COMPI enables it to automatically direct testing with various processes' executions as well as automatically determine the total number of processes used in the testing. Second, COMPI employs three techniques to effectively control the cost of testing as too high a cost may prevent its adoption. By capping input values, COMPI is made practical as too large an input can make the testing extremely slow and sometimes even fail as memory needed could exceed the computing platform's memory limit. With two-way instrumentation, we reduce the unnecessary memory and I/O overhead of COMPI and the target program. With constraint set reduction, COMPI keeps significantly fewer constraints by removing redundant ones in the presence of loops so as to avoid redundant tests against these branches. Our evaluation of COMPI uncovered four new bugs in a complex application and achieved 69-86% branch coverage which far exceeds the 1.8-38% coverage achieved via random testing.