A minimum description length (MDL) and stochastic complexity approach for model selection in robust linear regression is studied in this paper. Computational aspects and implementation of this approach to practical problems are the focuses of the study. Particularly, we provide both algorithms and a package of S language programs for computing the stochastic complexity and proceeding with the associated model selection. A simulation study is then presented for illustration and comparing the MDL approach with the commonly used AIC and BIC methods. Finally, an application is given to a physiological study of triathlon athletes.