The growth of bacterial colony exhibits striking complex patterns and robust scaling laws. Understanding the principles that underlie such growth has far-reaching consequences in biological and health sciences. In this work, we develop a mechanical theory of cell-cell and cell-environmental interactions and construct a hybrid three-dimensional computational model for the growth of {\it E.~coli} colony on a hard agar surface. Our model consists of microscopic descriptions of the growth, division, and movement of individual cells, and macroscopic diffusion equations for the nutrients. The cell movement is driven by the cellular mechanical interactions. Our unique treatment of the force arising from the liquid-air surface tension is applicable to both the monolayer (discrete) and multilayer (continuum) growth regimes. Our large-scale simulations and analysis predict the linear growth of the colony in both the radial and vertical directions, conforming the experimental observations. This work is the first step toward detailed computational modeling of bacterial growth with mechanical and biochemical interactions. This is joint work with Mya Warren, Hui Sun, Yue Yan, Jonas Cremer, and Terence Hwa.