The problem of free-form surface visualization and analysis is a very interesting task of computer graphics. The solving of this task is also actual in practical implementations (for example, biomedical engineering). The goal of this work is to develop new methods of interpolation and visualization of 3D objects. An effective method of 3D reconstruction is describe in this work using medical images of a brain acquired by computer tomography as an example. The proposed method is implemented for solving biomedical task. The method is based on construction of a sculpture surface interpolation model. In the result of this work a new method was developed. With the help of this method a free-form surface can be reconstructed using interpolation model. The reconstruction of the model is based on Coons surface. For further implementation the Coons surface model is transformed to Bezier surface. Using the proposed method, the model can be visualized with standard computer graphic tools. Standard computer graphics library OpenGL was used for visualization in this work. The acquired mathematical model can be used to analyze the object. The proposed method can be used in several spheres (science, medicine, engineering, etc.). Practical implementation of the proposed method is shown on the example of medical object. During implementation visualization using ray tracing was also realized.