Lead extrusion dampers are supplemental energy-dissipation devices that are used to mitigate seismic structural damage. Small volumetric sizes and high force capacities define high-force-to-volume (HF2V) devices, which can absorb significant response energy without sacrificial damage. However, the design of such devices for specific force capacities has proven difficult based on the complexities of their internal reaction mechanisms, leading to the adoption of empirical approaches. This study developed upper- and lower-bound force capacity estimates from analytical mechanics based on direct and indirect metal extrusion for guiding design. The derived equations are strictly functions of HF2V device geometric parameters, lead material properties, and extrusion mechanics. The upper-bound estimates from direct and indirect extrusion are denoted as (F_UB,1, F_UB,2) and (F_UB,3, F_UB,4), respectively, and the lower-bound estimates are denoted as (F_LB, F_LB,1) based on the combination of extrusion and friction forces. The proposed models were validated by comparing the predicted bounds to experimental force capacity data from 15 experimental HF2V device tests. The experimental device forces all lie above the lower-bound estimates (F_LB, F_LB,1) and below the upper-bound estimates (F_UB,1, F_UB,2, F_UB,4). Overall, the (F_LB, F_UB,2) pair provides wider bounds and the (F_LB,1, F_UB,4/F_UB,1) pair provides narrower bounds. The (F_LB,1, F_UB,1) pair has a mean lower-bound gap of 36%, meaning the lower bound was 74% of the actual device force on average. The mean upper-bound gap was 33%. The bulge area and cylinder diameter of HF2V devices are key parameters affecting device forces. These relatively tight bounds provide useful mechanics-based predictive design guides for ensuring that device forces are within the targeted design range after manufacturing.