We propose a procedure associated with the idea of the E-M algorithm for model selection in the presence of missing data. The idea extends the concept of parameters to include both the model and the parameters under the model, and thus allows the model to be part of the E-M iterations. Some special cases of the E-MS are considered, including the Markov-chain model for backcross experiments, and the linear regression model. We prove convergence of the E-MS algorithm. We address the issue regarding the missing data mechanisms. Furthermore, we carry out simulation studies on the finite-sample performance of the E-MS with comparisons to other procedures. A real data example is considered. This work is joint with Thuan Nguyen, Oregon Health & Science University, USA and J. Sunil Rao, University of Miami, USA.