Laser forming of non-developable surfaces necessitates simultaneous bending and shrinkage of the sheet blank. This can be obtained by coupling mechanism based laser forming. However, soft computing based modeling of this process as well as different laser parameter sets under coupling mechanism giving differentoptimum combinations of simultaneous bending and shrinkage is rarely reported. In this work, experiments have been carried out following a design of experiments with considered suitable ranges of the input factors, i.e., laser power, travel speed and laser beam diameter activating coupling mechanism. Response surface models for the outputs namely bending and thickening (resulted due to shrinkage) were developed in terms of the considered inputs and parametric effects were analyzed. Finite element modeling was also carried out to analyze thedeformation behavior. Multi-objective optimization of laser parameters for different combinations of maximum/ minimum of bending and thickening of the sheet material undergoing coupling mechanism has been shown. Forward and inverse models of the process have been built with the help of a backpropagation neural network (BPNN) and genetic algorithm-based neural network (GANN) based on experimental data. Because of the ability of genetic algorithm (GA) to obtain global search, GANN models provide better estimation of the input parameters for inverse modeling or process synthesis compared to that by the BPNN model. Finally, several dome-shaped surfaces were built with constant line energy but different Fourier numbers and hence, different proportions of bending and shrinkage. This was to demonstrate the importance of simultaneous bending and thickening of the sheet (achievable only by coupling mechanism) to generate such non-developable surface with minimal distortion.