Establishing the relationship between process parameters and the magnitude of residual stresses is essential to determine the life of welded components. It is the aim of this paper to develop mathematical models to assess residual stresses in the heat-affected zone of dissimilar butt jointed welds of AISI304 and AISI1016. These models determine the effect of process parameters on maximum residual stress. Laser power, travel speed and focal position are the process input parameters. Plates of 3 mm thick of both materials were laser welded using a 1.5 kW CW CO2 Rofin laser as a welding source. Hole-drilling method was used to compute the maximum principal stress in and around the HAZ of both sides of the joint. The experiment was designed based on a three factors five levels full central composite design (CCD). Twenty different welding runs were performed in a random order, 6 of them were centre point replicates and the maximum residual stresses were calculated for each sample. Design-expert software was used to fit the experiential data to a second order polynomial. Sequential F test and other adequacy measures were used to check the model’s performance. The results show that the developed models explain the residual stress successfully. Using the developed models, the main and interaction effect of the process input variables on the residual stresses at either side of the weld were investigated. It is found that all the investigated laser parameters are affecting the performance of the residual stress significantly.