High Force-to-Volume (HF2V) lead extrusion dampers can be used to protect structures by dissipating seismic response energy. The lead within the dampers deforms plastically by flowing around a bulged shaft, dissipating significant energy. This study develops a generic finite element modelling approach for these dampers to accurately predict device forces to optimize device designs for implementation into structures. A 2D axisymmetric large-deformation finite element model with adaptive meshing is developed using ABAQUS. The model has a rigid shaft and deformable working material (lead). The total force output is the sum of the contact frictional forces and contact pressure forces acting between the moving shaft and the displaced lead in the devices. For validation, model results are compared to experimental data from 14 experimental devices of different sizes and force capacities. The model predicts the force capacities of devices and simulates the stress distribution, and device behaviour with good overall accuracy. Model force-displacement plots exhibits good prediction capacity corresponding to experimental results. The error in predicted force capacity for 10 of the 14 modelled devices is less than 10%, with 3 further devices within 10%-20% errors and the one within 30% errors. Overall, a generic FEM modelling approach for highly nonlinear HF2V devices is developed, with very good performance compared to experimental data. This modelling approach enables improved optimization of device design for developing a specific design for buildings or bridges using these devices.