Thermomechanical models are presented for the building of thin-walled structures by laser-based solid freeform fabrication (SFF) processes. Thermal simulations are used to develop quasi-non-dimensional plots (termed process maps) that quantify the effects of changes in wall height, laser power, deposition speed, and part preheating on thermal gradients, with the goal of limiting residual stresses in manufactured components. Mechanical simulations are used to demonstrate the link between thermal gradients and maximum final residual stresses. The approach taken is analogous to that taken in previous research by the authors in developing process maps for melt pool length, for maintaining an optimal melt pool size during component fabrication. Process maps are tailored for application to the laser engineered net shaping process; however, the general approach, insights, and conclusions are applicable to most SFF processes involving a moving heat source, and to other laser-based fusion processes. Results from the residual stress simulations identify two mechanisms for reducing residual stresses and quantify maximum stress reductions achievable through manipulation of all process variables. Results from thermal gradient and melt pool length process maps are used to identify a manufacturing strategy for obtaining a consistent melt pool size while limiting residual stress in a thin-walled part.