In this study, a mathematical model is developed for determining the process parameters used in the manufacturing process of powder materials with selective laser melting method. Although the studies carried out to date cover detailed modeling studies including three-dimensional and time-dependent situations, obtaining quite different approaches from experimental results has led to the idea that a change should be made in the construction of the mathematical problem. Therefore, different from other studies and for the first time, the Eigen-function expansion method was used in the analytical solution of the selective laser melting thermal model. The developed mathematical model includes the steady-state solution with the appropriate boundary conditions of the 2-D non-homogeneous heat equation. The mathematical model was first solved analytically with the Eigen-function expansion method, and the function obtained as a result of the solution was introduced into the MATLAB software. The parametric study was performed numerically over laser power, laser spot size and powder bed thickness. With the developed model, the solution was converged in 30 s and 11.5% more accurate with respect to experimental results were obtained in width, 29% in depth and 3% in temperature as compared to other analytical models exist in the literature.