Variable selection algorithm for Sliced Inverse Regression using penalty function is proposed. We noted SIR models can be expressed as generalized eigenvalue decompositions and incorporated penalty functions on them. We found from small simulation that the HARD penalty function seems to be the best in preserving original directions compared with other well-known penalty functions. Also it turned out to be effective in forcing coefficient estimates zero for irrelevant predictors in regression analysis. Results from illustrative examples of simulated and real data sets will be provided.