The orthotropic plate with intermediate point supports has extensive applications in construction of deck of bridges, wings of airplanes, body of ships and rockets. Plates with point supports are not readily amenable to solution because the concentrated shear force at the point supports locations makes discontinuous force field on the plate. For this reason making the equilibrium conditions on the point supports in the ordinary continuum plate analysis couldn’t be straightforward. In this study elastic buckling of orthotropic plates with various geometries and intermediate point supports is investigated. Hp-Cloud shape functions are used to approximate the displacement. Some of the great advantages of Hp-cloud approach include possibility to make approximation functions with desirable continuity by means of making the appropriate weighting functions and selection of proper enrichment functions, possibility to improve approximation procedure by reducing the influence radius (h-refinement) and increasing the monomials or changing the type of enrichment function (p-refinement), accessing to shape functions of the nodes without any inverting operation due to selecting Shepard functions as the partition of unity and local approximation norm of the Hp-cloud shape functions that reduce density of elastic and geometry stiffness matrix. In this study by selecting the special pattern for influence radius of nodes and polynomial type of enrichment function, Hp-cloud shape functions with kronecker delta property are constructed. Therefore it is feasible to satisfy zero displacement condition in point supports location that is placed on the field nodes. It must be noted that there are some geometric constraints in constructing Hp-cloud shape functions with kronecker delta property. So in general more considerations for satisfying essential boundary condition are needed. In this case the Lagrange multiplier method has been used. justify; LINE-HEIGHT: normal; TEXT-INDENT: 0in; MARGIN: 0in 0in 0pt; unicode-bidi: embed; DIRECTION: ltr; tab-stops: 373.5pt" For calculating the elastic and geometry stiffness matrix elements one must integrate on the subscription surface of two corresponding clouds. In this study refined cell structure method is introduced for numerical integration. In the refined cell structure method, first the subscription surface of two clouds is divided in number of segments. Again every segment that is in conjunction with the boundary of plates is divided in order to access more exact consideration of real surface of integration. Proper results are achieved by the use of refined cell structure for solving the plate with complex geometry just like regular geometric one. Equivalent distribution of one and two row point supports on the plate edges for modeling the ordinary simply supported and clamped supported boundary condition is indicated by comparing buckling coefficients of two manners. Tendency of boundary conditions of plate edges with periodic distribution of point supports toward simply supported condition is studied for various shapes of trilateral and quadrilateral plates. Buckling modes and behavior of plates are also examined under in-plane forces such as uniaxial pressure, biaxial pressure, shear, bending and interaction of these forces. Furthermore, interaction curves of in-plane forces are plotted for corner supported plates with different geometry. Keywords : Elastic buckling, plates with various shapes, intermediate point supports, Hp-cloud shape functions, Ritz method.