It is possible to resolve numerical issues by utilizing a method known as the conventional scaled boundary finite element method (also known as SBFEM), which is a dimension reduction technique. This method can be utilized in conjunction with mesh-free technologies to enhance the numerical characteristics of the conventional SBFEM. Within the scope of this investigation, a novel interpretation of the SBM is presented that makes use of the advantages offered by the meshless local Petrov Galerkin method. Using the moving Kriging interpolation (MKI) method, one can create shape functions that conform to the requirements of the Kronecker delta function property. The interpolating scaled boundary local Petrov Galerkin method that was proposed then can implement essential boundary conditions (ISBLPGM) directly. This new method offers a number of benefits in comparison to scaled boundary approaches that have been presented in the past. It is optional to have a mesh that has been predefined, and the boundary conditions can be determined with very little additional effort. It has been demonstrated that the numerical approach that is being presented yields results that are in very good agreement with analytical and other numerical approaches. Solving the benchmark numerical problems allows for an evaluation of the effectiveness of the proposed method as well as its precision