This study presents first principles derivation of the partial differential equations (PDEs) for flexural solutions of Mindlin’s first order shear deformation plate theory (MFSDPT). The PDEs were formulated using the kinematics, constitutive and equilibrium equations in an equilibrium approach. The resulting PDEs are coupled system of three PDEs in three unknown displacements – one transverse displacement w and two rotations and The study considered a simply supported thick plate bending problem for illustrative solutions. Double finite sine transformation methodology (DFSTM) was utilized for solutions in that double sine kernel functions of the transformation satisfies the simply supported boundary conditions. The DFSTM simplified the system of PDEs to a system of three algebraic equations with displacement amplitudes Wmn, Amn and Bmn for w, and respectively. Analytical solutions were obtained for uniformly and linearly distributed loadings transversely applied on the domain. The present results for in-plane and transverse displacements are comparable to previously obtained results. The MFSDPT results are closed form in the theoretical framing of small displacement elasticity theory for homogeneous, isotropic thick plates. The DFSTM has been shown to give accurate solutions to the resulting equations.