Low-inductance solenoidal coils, which usually refer to the nonintersecting type and the braid type, have already been employed to build superconducting fault current limiters because of their fast recovery and low inductance characteristics. However, despite their usage there is still no systematical simulation work concerning the AC loss characteristics of the coils built with 2G high temperature superconducting tapes perhaps because of their complicated structure. In this paper, a new method is proposed to simulate both types of coils with 2D axisymmetric models solved by H formulation. Following the simulation work, AC losses of both types of low inductance solenoidal coils are compared numerically and experimentally, which verify that the model works well in simulating non-inductive coils. Finally, simulation works show that pitch has significant impact to AC loss of both types of coils and the inter-layer separation has different impact to the AC loss of braid type of coil in case of different applied currents. The model provides an effective tool for the design optimisation of SFCLs built with non-inductive solenoidal coils.