In this part of the paper, we introduce a meshfree approach for static analysis of isotropic/orthotropic cross-ply laminated plates with symmetric/non-symmetric layers. In this method, the solution is first split into homogenous and particular parts and then the homogenous part is approximated by the summation of an appropriately selected set of exponential basis functions (EBFs) that are restricted to satisfy the governing partial differential equation (PDE). The particular solution is derived using a similar approach and another series of EBFs. The imposition of the boundary conditions is performed by a collocation method through a discrete transformation technique. The solution method allows us to obtain semi-analytical solution of plate problems with various shapes and boundary conditions. Although implemented for cross-ply laminates in this work, the proposed method is applicable to more general lamination cases as long as the governing PDEs are of constant coefficient type. This part of the paper is devoted to the basic features of the formulation and the evaluation of the EBFs using classical, first and third order shear deformation theories. Explicit expressions are given for special cases for further use.