Surface modeling is one of the most important stages in the design of mechanical parts, especially in creating free-form surfaces such as car bodies, ship and boat hulls, blade forms, bottle bodies, and the like, which are important in terms of both aesthetics and engineering. In this study, a method for manipulating and optimizing surfaces with constrained boundaries using a combination of the Coons and Bezier methods as well as Coons and Hermite bicubic is presented. In this method, first, based on the constrained boundaries, an initial Coons surface is created and then decomposed into several arbitrary Bezier or Hermite bicubic patches for surface manipulation. Bezier patches are created solely by points taken from the surface, whereas to create Hermite bicubic patches, the first and second tangent vectors must be calculated in addition to the points. Accordingly, the results obtained show that the combination of the two methods, the Coons method and the Hermite bicubic, provides a smooth surface with continuity of the first-order derivative at all points based on constrained boundary curves, where the combination of the two methods, the Coons and Bézier, has the property of easier control of points, but at the boundary where the patches connect inside the surface, there is no requirement for continuity of the first-order derivative.