A new, dynamic, double-input, double-output (DIDO), wideband, dynamic, complex envelope, behavioral model for power amplifiers (PAs), accounting for load mismatch effects, is proposed and validated in this paper. The model is constructed based on two-dimensional, dynamic, canonical section-wise piecewise-linear functions (2-D DCSWPL). Compared with existing DIDO behavioral modeling methods, which are almost all exclusively based on polynomial functions, the proposed model permits a vastly extended modeling space for PAs under load mismatch conditions. Experimental examples are given to validate the proposed modeling technique with a 15 W GaN PA under a wide range of output mismatch conditions, driven by a 5 MHz LTE signal. The proposed model shows an average accuracy improvement of 2 dB when compared with the more traditional DIDO memory polynomial (MP) models. In addition, the load reflection-dependent dynamic 2-D CSWPL modeling technique for PAs under mismatch condition is also provided. Compared with load-dependent MP, load-dependent crossover MP (COMP) and load-dependent DIDO MP models, the proposed model shows superior accuracy. Thus, the proposed modeling technique is an excellent choice for the modelling of PA systems that are subject to load mismatch effects. INDEX TERMS Canonical section-wise piecewise-linear Function, dynamic modeling, load mismatch effects, nonlinear behavioral Modeling, RF PAs.