Epithelial invagination is one of the fundamental deformation modes during morphogenesis, and is essential for deriving the three-dimensional shapes of organs from a flat epithelial sheet. Invagination occurs in an orderly manner according to the spatial pattern of the contractile cells; however, it remains elusive how tissue deformation can be caused by cellular activity in the patterned region. In this study, we investigated the mechanical role of the spatial patterns of the contractile cells in invagination of growing tissue using multicellular dynamics simulations. We found that cell proliferation and apical constriction were responsible for expanding the degree of tissue deformation and determining the location of the deformation, respectively. The direction of invagination depended on the spatial pattern of the contractile cells. Further, comparing the simulation results of surface and line contractions as possible modes of apical constriction, we found that the direction of invagination differed between these two modes even if the spatial pattern was the same. These results indicate that the buckling of the epithelial cell sheet caused by cell proliferation causes the invagination, with the direction and location determined by the configuration of the wedge-shaped cells given by the spatial pattern of the contractile cells.