Operating circuits in the near/sub-threshold regime can lower the circuit energy consumption at the expense of lowering the circuit speed. In addition near/sub-threshold can result in higher sensitivity to process-induced variations and transient noise. FinFETs have been proposed as an alternative to planar CMOS devices in sub-20nm CMOS technology nodes due to their more effective channel control, steep sub-threshold slope, high ON/OFF current ratio, low power consumption, and so on. Characteristics of FinFETs operating in the near/sub-threshold regime make it difficult to verify the timing of a circuit using conventional statistical static timing analysis (SSTA) techniques. Current source modeling (CSM) methods, which have been proposed to increase the accuracy of timing analysis in dealing with arbitrary shapes of the input signal waveforms, are the appropriate solution for performing SSTA on FinFET-based circuits. This paper thus extends the CSM to such circuits, operating in the near/sub-threshold voltage regime. In particular, FinFET devices with independent gate control and subject to process variations are modelled. The key idea of the proposed CSM approach is to combine non-linear analytical models and low-dimensional CSM lookup tables to simultaneously achieve high modeling accuracy and low time/space complexity.