The deflection of thin orthotropic rectangular plate under moving loads is a classic problem in solid mechanics. However, the equations are challenging to solve due to their non linearity and complexity. At the same time, this equation is a coupled fourth order partial differential equation having variables and singular coefficients. In this research article, the partial differential equation is converted to a set of coupled second order ordinary differential equations by using a special technique adopted by Shadnam et al., [19]. This transformed set of second order ordinary differential equations is then reduced using modified asymptotic method of Struble and Laplce transformation. The closed form solution is evaluated, resonance conditions are obtained and the results are showed in plotted curves to solve the variations in amplitudes for some varying orthotropic plate parameters with elastically supported ends under moving loads for both cases of moving distributed force and moving distributed mass.