The present work is an experimental investigation on the laser forming process of aluminum alloy and stainless-steel thin sheets. A high-power diode laser (HPDL) with a nonsymmetric spot configuration was employed at medium and low scanning rates. The tests were performed at different operating conditions: scanning rate, laser spot orientation, and laser beam power. The experimental results revealed the great influence of the laser spot orientation on the total bending angle and the harmful effect of the surface melting during heating. Spot orientation significantly affects the treated area extension during laser scanning. Employing an analytical thermo-mechanical model, a dimensionless processing map can be presented that allows the prediction of the sheet bending angle depending on the material properties and machining parameters. Dimensional terms of the processing map can be associated to efficiency terms for heat transfer and bending.