We apply a stochastic mode reduction procedure to obtain simplified equations for the dynamics of structures immersed in a thermally fluctuating fluid at low Kubo (or Reynolds) number under the Immersed Boundary method. This computational framework was developed with Charles Peskin primarily for simulating processes occuring within biological cells, such as molecular motor transport, but applies more generally to fluids with flexible immersed structures where thermal fluctuations play a significant role. The simplified dynamics obtained through the stochastic mode reduction procedure reveal the features of the long-time behavior of the immersed structures simulated by the Immersed Boundary method (including the effects of spatial discretization), and thereby inform physically appropriate choices of parameters and indicate future directions for improvement of the numerical method. The analysis of the Immersed Boundary method through the stochastic mode reduction procedure is joint work with Andrew Majda.