State Transition Matrix (STM) is a table-based modeling language for developing designs of software systems. Although widely accepted and used in software industry, there is lack of formal verification supports for conducting rigorous analysis to improve reliability of STM designs. In this paper, we present a symbolic encoding approach for STM designs that employ message passing as the means of communication, through which correctness of a STM design with respect to invariant properties could be Bounded Model Checked (BMC) by using Satisfiability Modulo Theories (SMT) solving techniques. We have built a prototype implementation of the proposed encoding and the state-of-the-art SMT solver - Yices, is used in our experiments as a back-end tool to evaluate the effectiveness of our approach. In addition, two approaches for accelerating SMT solving by introducing additional knowledge are proposed and their effectiveness is shown by our preliminary experimental results.