One of the critical issues in numerical simulation of fluid-structure interaction problems is inaccuracy of the solutions, especially for flows past a stationary thin elastic structure where large deformations occur. High resolution is required to capture the flow characteristics near the fluid-structure interface to enhance accuracy of the solutions within proximity of the thin deformable body. Hence, in this work, an algorithm is developed to simulate fluid-structure interactions of moving deformable structures with very thin thicknesses. In this algorithm, adaptive mesh refinement (AMR) is integrated with immersed boundary finite element method (IBFEM) with two-stage pressure-velocity corrections. Despite successive interpolation of the flow field by IBM, the governing equations were solved using a fixed structured mesh, which significantly reduces the computational time associated with mesh reconstruction. The cut-cell IBM is used to predict the body forces while FEM is used to predict deformation of the thin elastic structure in order to integrate the motions of the fluid and solid at the interface. AMR is used to discretize the governing equations and obtain solutions that efficiently capture the thin boundary layer at the fluid-solid interface. The AMR-IBFEM algorithm is first verified by comparing the drag coefficient, lift coefficient, and Strouhal number for a benchmark case (laminar flow past a circular cylinder at Re = 100) and the results showed good agreement with those of other researchers. The algorithm is then used to simulate 2-D laminar flows past stationary and moving thin structures positioned perpendicular to the freestream direction. The results also showed good agreement with those obtained from the arbitrary Lagrangian-Eulerian (ALE) algorithm for elastic thin boundaries. It is concluded that the AMR-IBFEM algorithm is capable of predicting the characteristics of laminar flow past an elastic structure with acceptable accuracy (error of �0.02) with only �1 of the computational time for simulations with full mesh refinement. © 2020, China Ship Scientific Research Center.