Over the years, wings have become lighter and more flexible, making them more prone to aeroelastic effects. Thus, aeroelasticity in design becomes more important. In order to determine the response of an aircraft to, for example, a gust, an unsteady aerodynamic model is required to determine the dynamic loads. The three most-commonly used methods in aeroelastic loads analysis are 2D unsteady-airfoil theory, the doublet lattice method (DLM), and the unsteady vortex lattice method (UVLM). In contrast to these existing methods, the current paper proposes a 3D state-space model for unsteady aerodynamic analysis that is both directly written in time-domain, and is a continuous-time model. The main advantages of this are that no approximation errors are made in the conversion to the time domain, and that the time step is only driven by requirements on accuracy. The model is based on potential flow theory, which is implemented by means of vortex ring elements. The model was first verified, and then applied to a pitch-plunge response problem showing the benefits of the current approach over existing methods.