A molded cementitious architectural product for use in building construction has a cementitious body made of a molded cementitious material, the surface of which is polished (i.e., burnished) to better resemble natural stone. The polished surface is formed by exposing a portion of the molded cementitious material while in a green condition, more particularly after initial set but before final hardening of the hydraulic cement binder, and burnishing the surface before final hardening. Burnishing the surface of the green cementitious material before final hardening aligns the cement particles at the surface and seals the surface. The inclusion of an organic polymer binder within the cementitious material, such as an acrylic or latex polymer, assists in creating a polished surface resembling natural polished stone. The extent of cement hydration may be determined by monitoring the temperature of the cementitious material within the mold. Hydration may be slowed by quenching the molded green cementitious material with water to extend the window of time within which burnishing may be carried out before reaching final hardening.