In this dissertation, along with a thorough investigation on the advantages and disadvantages of the Iso-Geometric Analysis (IGA) method and a meshless method based on using Exponential Basis Function (EBFs), two novel forms of the mesh-free method using the EBFs, equipped with tools for definition of the geometries, are presented. The proposed methods enables the users to solve 3D problems in physics through grid generation in CAD. In the first method, the grid of nodes corresponding to the 3D domain is generated through a discrete searching algorithm. The Non-Uniform Rational B-Spline functions (NURBS), solely as a choice among the similar tools, are employed in construction of the boundary surfaces of the domain. Then a pre-defined regular grid of nodes, embedding the whole of the domain’s geometry, is trimmed by the boundary surfaces. The spatial solution is also approximated by collocating a set of rationally chosen EBFs on the nodes of each individual local cloud of points conforming to the domain boundaries. The proposed approximation bases, satisfying the homogeneous part of the governing partial differential equation (PDE), form a set of rational shape function which have the Partition of Unity and Kronecker delta properties. While all the aforementioned properties make the proposed mesh-free method effective in the numerical solution of 3D problems, the last one facilitates direct imposition of Dirichlet boundary conditions. By establishing the compatibility conditions between the clouds and satisfying the remaining boundary conditions a linear sparse system of equations is constructed and solved numerically. To illustrate the efficiency of the proposed method, the numerical solutions for Laplace, Helmholtz and Elasticity problems, defined on 2D/3D domains, are obtained. Some discussions are provided on the accuracy and the convergence of the results using the available analytical solutions or the approximate ones found by some commercial softwares. The second method is proposed for the solution of problems defined on more complex 3D geometries such as those with cellular materials. Firstly, the NURBS object or an imaged-based geometry, such as a micro-CT scan image, is embedded in a regular grid of nodes and then a non-boundary fitted discretization approach is simply accomplished. Afterward, with the library rational shape functions defined in the first method (collocation method) in hand, the solution of the problem is approximated on the overlapping clouds covering the domain by adding some modified singular basis functions to satisfy the boundary conditions. In this line, the properties and benefits of utilizing the supplemented singular basis functions are briefly discussed while the physical coordinates and the appropriate loci of singularities are determined. The unknown coefficients corresponding to the nodes falling outside of the domain and also the singular bases defined for each local cloud are calculated, in terms of nodal values on nodes inside the domain, by a weighted least square approach for the residuals of the boundary conditions on the boundary voxels of the domain. With this modification for the satisfaction of the boundary conditions in complex geometries, the rest of the solution method follows that of the first method. In this thesis, the convergence of the approximated solution found by the second proposed mesh-free method to the exact solution of Laplace equation on different geometries is investigated. Also, the solutions of some realistically defined steady-state heat problems on complex geometries namely, closed foams (perforated plate), open foams (honey comb) and 3D foams are evaluated and compared with the approximated solutions evaluated by the Finite Element Method. Key Words Meshless Method, complex geometry, exponential basis functions, 3D problems, grid generation