An efficient Galerkin meshfree flat shell formulation is presented for the analysis of buckling behaviors of stiffened plate structures. Both plate bending and membrane deformations are approximated by the reproducing kernel particle method (RKPM). The governing equation is transformed into a weak,form, and it is discretized by the scattered nodes. The stiffness matrix is numerically integrated with the nodal integration technique, i.e., the stabilized conforming nodal integration (SCNI). The RKPM and SCNI based flat shell modeling approach can address the shear locking problem. Additionally, the present discretization is further improved by involving a drilling rotation component, which is to effectively model the stiffeners. There are six degrees of freedom per node. A singular kernel is also introduced into a set of the interpolants to model the web/flange connection, as well as the imposition of the essential boundary conditions. A generalized eigenvalue problem is analyzed for evaluating buckling loads/modes of the stiffened plate structures. The accuracy of the numerical results and the effectiveness of the proposed method are examined through several numerical examples.