This paper develops a dynamic stochastic general equilibrium model with putty-clay technology that incorporates embodied technology, investment irreversibility, and variable capacity utilization. Low short-run capital-labor substitutability native to the putty-clay framework induces the putty-clay effect of a tight link between changes in capacity and movements in employment and output. As a result, persistent shocks to technology or factor prices generate business cycle dynamics absent in standard neoclassical models, including a prolonged hump-shaped response of hours, persistence in output growth, and positive comovement in the forecastable components of output and hours. Capacity constraints result in a nonlinear aggregate production function that implies asymmetric responses to large shocks with recessions steeper and deeper than expansions. Minimum distance estimation of a two-sector model that nests putty-clay and neoclassical production technologies supports a significant role for putty-clay capital in explaining business cycle and medium-run dynamics.