Laser bending is an innovative technique to obtain the required bend-angle and sheet metal curvature by means of laser beam irradiation with controlled laser parameters. In this work, a numerical investigation on curvilinear laser bending of magnesium M1A alloy sheets has been carried out. Three-dimensional sequential transient thermomechanical numerical model is developed by using finite element method. The model has been validated by comparing the predicted results with those obtained in the experiments. The curvilinear laser bending process is studied in terms of temperature distribution, stress–strain distribution, bend angle and displacement at the edges. The results showed that the bend angle increases with increase in scanning path curvature. It is observed that the displacement at various edges and final shape of the worksheet are affected by the scanning path curvature. The results will be useful in adjustment and alignment processes and the generation of complex shapes using lasers.