We formulated a spatially resolved model to estimate forces exerted by a polymerizing actin meshwork on an invagination of the plasma membrane during endocytosis in yeast cells. The model, which approximates the actin meshwork as a visco-active gel exerting forces on a rigid spherocylinder representing the endocytic invagination, is tightly constrained by experimental data. Simulations of the model produce forces that can overcome resistance of turgor pressure in yeast cells. Strong forces emerge due to the high density of polymerized actin in the vicinity of the invagination and because of entanglement of the meshwork due to its dendritic structure and cross-linking. The model predicts forces orthogonal to the invagination that are consistent with formation of a flask shape, which would diminish the net force due to turgor pressure. Simulations of the model with either two rings of nucleation-promoting factors (NPFs) as in fission yeast or a single ring of NPFs as in budding yeast produce enough force to elongate the invagination against the turgor pressure.