Actual vehicle-to-vehicle (V2V) channel measurements have shown that the wide-sense stationary (WSS) modeling assumption is valid only for very short time intervals. This fact motivates us to develop non-WSS V2V channel models. In this paper, we propose a novel three-dimensional (3D) theoretical non-WSS regular-shaped geometry-based stochastic model (RS-GBSM) and the corresponding sum-of-sinusoids (SoS) simulation model for non-isotropic scattering wideband multiple-input multiple-output (MIMO) V2V fading channels. The movements of the transmitter (Tx), scatterers, and receiver (Rx) result in the time-varying angles of departure (AoDs) and angles of arrival (AoAs) that make our models non-stationary. The proposed RS-GBSMs, combining line-of-sight (LoS) components, a two-sphere model, and multiple confocal elliptic-cylinder models, have the ability to study the impacts of vehicular traffic density (VTD) and non-stationarity on channel statistics, and jointly consider the azimuth and elevation angles by using the von Mises Fisher (VMF) distribution. The proposed RS-GBSMs are sufficiently generic and adaptable to model various V2V scenarios. Based on the proposed 3D non-WSS RS-GBSMs, important local channel statistical properties are derived and thoroughly investigated. The impacts of VTD and non-stationarity on these channel statistical properties are investigated by comparing them with those of the corresponding WSS model. The proposed non-WSS RS-GBSMs are validated by measurements in terms of the channel stationary time. Finally, numerical and simulation results demonstrate that the 3D non-WSS model is more practical to characterize real V2V channels.