Many physical and engineering problems require solving complex differential equations on a physical space. For instance, computational fluid dynamics and other simulation techniques can be mentioned, which use numerical techniques to solve such problems. The first step in using numerical techniques is the modeling of the physical space. This is a formidable task for complex geometries and free shape objects.In this thesis, different techniques used in solid modeling are reviewed and the most advanced technique (i.e. NURBS) is presented in details. NURBS is the industry de facto standard and is used in most CAD and CAM software. Several techniques to generate NURBS curves, surfaces and volumes have been studied and implemented in a matlab library of functions. Then different techniques to arbitrarily distribute points on a NURBS curve are introduced. In addition, some algebraic and elliptic grid generation routines are developed to create high quality grids on NURBS surfaces. The Nurbs format provides a common mathematical representation for both standard analytic shapes and free-form curves and surfaces. The derivatives of the physical coordinates with respect to the parametric coordinates can be evaluated directly.High fidelity simulations using mesh-based computational technologies such as computational fluid dynamics and computational structural mechanics are very important in providing valuable performance information of a design. These simulations, however, require accurate geometry representation as well as high quality meshes about the design in order to obtain accurate data. Next using some algebraic methods, capable us to generate initial grid on Nurbs surface. Finally we will have a survey on elliptic method for grid generation. For grid generation by means of elliptic method we need control functions for some states such as orthogonality, smoothness, concentration. By using whole of algorithms with respect to aforementioned parts and referenced algorithms, we write some codes in MATLAB which are capable modeling a many number of curves, surfaces and volumes and generating grid on this modeled surfaces in some different states.In this thesis the elliptic method for grid generation was selected. In this method, some control function should be considered. The control functions usually are used for some cases such as orthogonality, smoothness and concentration. Finally a matlab code is prepared by using an aforementioned algorithm. This code can model complicated surfaces and volumes and generate grid on them. Keywords: Nurbs Modeling, Point Distribution On Nurbs Curves, Structured Grid Generation, Algebraic Grid Generation, Arc Length Based Grid Generation, Elliptic Grid Generation.