This study addresses in-plane thermal residual stresses in two-dimensional functionally graded plates under a constant in-plane heat flux. The plate material properties vary with a power law along two in-plane directions not through the plate thickness. The transient heat conduction and Elasticity's Navier equations describing the two-dimensional the rmo-elastic problem were discretized using the finite-difference method, and the set of linear equations was solved using the pseudo singular value method. The in-plane transient distributions of temperature, displacement, stress and strain components were determined, and the two-dimensional exponents and directions of compositional gradient were investigated in terms of their effects on the stress and strain distributions in both plates. The exponent and direction of the compositional gradient affected the peak in-plane strain and stress levels; therefore, the stress and strain distributions can be relieved by arranging the exponent and directions of the compositional gradient.