Due to the rational form of shape functions, traditional Galerkin-type meshfree methods face challenges in achieving precise numerical integration. We propose a novel meshfree stabilized collocation method that employs reproducing kernel approximation or Lagrangian interpolation as approximation functions. By adopting a subdomain approach and performing subdomain integration of the strong form, this method enables accurate integration, thereby enhancing the algorithm's precision and stability. Subdomain integration also helps reduce the condition number of the discrete matrix, further improving numerical stability. Moreover, accurate integration can be achieved using low-order Gaussian quadrature, which enhances computational efficiency. This approach combines the high efficiency of collocation-type mesh-free methods with the high accuracy and robustness of Galerkin-type mesh-free methods, while also incorporating the feature of local conservation of discrete equations characteristic of the finite volume method, making it applicable to both solid and fluid mechanics analyses. We developed a gradient-smoothed stabilized collocation method to improve computational efficiency and convergence rates. Since the integration subdomains in the stabilized collocation method are solely determined by the collocation point positions and do not deform during domain deformation, this method effectively circumvents the need for remeshing integration grids in traditional mesh-free approaches when solving large deformation problems, significantly enhancing the efficiency of extreme large deformation analyses. We also propose a Lagrangian-Eulerian stabilized collocation method. This method employs a Lagrangian-Eulerian description, solving the governing equations for fluids, solids, and their coupling on Eulerian nodes via the stabilized collocation approach. It eliminates the need to reconstruct shape functions at each time step, thus improving computational efficiency. By utilizing high-order mapping functions, the method preserves high-order accuracy in mapping while ensuring mass and momentum conservation. This framework enables efficient and high-precision numerical analysis of fluid flows with free surfaces and fluid-structure interaction problems. To address discontinuous problems such as shock waves, we further propose a discontinuous stabilized collocation method, which enables high-precision simulation of explosion phenomena.