This thesis deals with 2-dimensional unsteady flows around bodies with relative motion. The unsteady compressible inviscid equations are solved by an explicit finite volume, upwind method using unstructured dynamic meshes. The combination of remeshing technique and window concept is implemented for efficient calculations. The mesh adaptation is achieved by local addition of points, using an error estimation procedures and triangulating all the points on the computational domain. The resulting scheme allows economic simulations of fully coupled fluid-rigid body interaction problems of arbitrary geometric complexity. The numerical method is applied for one or two body problems such as pitching and plunging airfoils. The results of a sinusoidally pitching airfoil problem are compared with experimental data for validations.