Beams, as flat slender structures primarily subjected to bending and transverse shear stresses and likely used in every engineering structure, are among the most important topics in mechanical and structural engineering training and practice today. Despite the long history of man's understanding of structural behavior and the various shear deformation theories for beams proposed, the Euler–Bernoulli beam theory (or classical beam theory) is still the most widely used engineering approach today. Although the finite element method (FEM) is now the standard engineering method for analyzing all types of beam problems, meshfree methods have also been used to analyze beams in recent years. The assumption that any function can be written as an expansion of a set of continuously differentiable basis functions is a simple, easy to implement, and very popular non-symmetric meshless method for solving partial differential equations (PDEs) nowadays which, provided the basis coefficients are properly determined by a collocation method, can, in general, be used as an approximation scheme for the solution of PDEs. This article addresses radial point collocation numerical technologies for the static analysis of Euler–Bernoulli beams involving fourth-order spatial derivatives, including how to apply the method to uniform and isotropic beams with arbitrary boundary conditions and loadings, as well as a performance comparison of the meshless approach to traditional analytical and FEM solutions, demonstrating its appeal and competitiveness for a broader engineering application.