An unsteady low-order panel method for three-dimensional subsonic analyses is presented. The method, which is based on well-established techniques in computational aerodynamics, is intended to achieve a cost-effective solution of unsteady flows around arbitrary aerodynamic configurations. This work has two main objectives. First, to relax geometry discretization requirements and, second, to simplify the treatment of problems in which the analysis configuration moves along specified flight paths and/or changes its geometry during the simulation. Following this aim, a time-marching solution procedure is adopted in conjunction with a free-wake model which avoids iterative solutions for wake shape and position. The suitability of the present approach for solving typical aerodynamic problems is illustrated by means of several numerical examples.