This paper is concerned with finite element Galerkin approximations for a fluid-solid interaction model. Both continuous-time and discrete-time approximations are formulated and analyzed, and optimal order a priori estimates for the errors in \(L^\infty(H^1)\) and \(L^\infty(L^2)\) are derived. The main difficulty for the error estimates is caused by interface conditions which describe the interaction between fluid and solid on their contact surface. This difficulty is overcome by using a boundary duality argument of J. Douglas jun. and T. Dupont [Numer. Math. 20, 213-237 (1973; Zbl 0234.65096)] to handle the terms involving the interface conditions. The author also proposes parallelizable domain decomposition algorithms for efficiently solving the arising finite element systems.