Dynamic Materials Model (DMM) processing maps are useful for identifying a large window for "safe" processing of materials. It is usually difficult to control the microstructure of the product if the processing window is large. A new methodology which uses an apparent activation energy for deformation and a model for the evolution of microstructure has been proposed to refine the large window and also to control the final microstructure of the product. The usefulness of the proposed methodology for designing hot extrusion process has been demonstrated for 304L stainless steel. The deformation behavior of 304L stainless steel was evaluated in the temperature range of 600degreesC to 1200degreesC and the strain-rate range of 0.001 s(-1) to 100 s(-1) with a view to generating DMM processing maps. From the processing maps, a window in the temperature range of 1000degreesC to 1200degreesC and strain-rate of 0.01 s(-1) to 10 s(-1) is identified as a 'safe' domain for hot working. This "safe" processing regime has been further refined by using the value of an apparent activation energy for deformation. In order to control the final microstructure of the product, an analytical model for the evolution of microstructure during hot working (in the refined domain) was obtained. Using the above model, the optimum strain, strain-rate, and temperature trajectories were arrived at for obtaining a grain size of 35 mum in an extruded product. Process control parameters, such as ram velocity, die profile and billet temperature, which achieve the optimal trajectories were calculated using a process model. Extrusion trials were conducted at the optimal conditions and a good agreement with those predicted in the design stage has been achieved.