The budding yeast, Saccharomyces cerevisiae, is a prime biological model to study mechanisms underlying asymmetric growth. Previous studies have shown that, prior to yeast bud emergence, polarization of a conserved small GTPase, Cdc42, must be established. Additionally, hydrolase changes the mechanical properties of the cell wall and plasma membrane with the periplasm between them (cell surface). However, how the surface mechanical properties in the emerging bud are different from the properties of the mother cell and their role in bud formation are not well understood. We hypothesize that the polarized chemical signal alters the local dimensionless ratio of stretching to bending stiffness of the cell surface of the emerging yeast bud. To test this hypothesis, a novel three-dimensional coarse-grained particle-based model has been developed which describes inhomogeneous mechanical properties of the cell surface. Model simulations suggest that regulation of the dimensionless ratio of stretching to bending stiffness of the cell surface is necessary to initiate bud formation . Furthermore, model simulations predict that bud shape depends strongly on the experimentally observed molecular distribution of the polarized signaling molecule Cdc42, while the neck shape of the emerging bud is strongly impacted by the properties of the chitin and septin ring. This 3D model of asymmetric cell growth can also be used for studying viral budding and other vegetative reproduction processes performed via budding.