Buried pipeline systems are increasingly exposed to compound geohazards, particularly the interaction between earthquake ground motions and moisture-induced swelling of expansive soils. Despite their prevalence, these hazards are commonly treated independently in computational analyses. This study presents a computational mechanics framework for multi-hazard fragility assessment of buried pipelines that explicitly couples swelling-induced ground deformation with seismic loading. A three-dimensional finite-element (FE) soil–pipe interaction model is developed to capture nonlinear soil behavior, frictional pipe–soil contact, and staged loading. Swelling is simulated through imposed volumetric strain within a Mohr–Coulomb soil continuum to represent moisture-driven expansion, followed by dynamic excitation using applied earthquake acceleration-time histories. To efficiently sample the coupled hazard space, the FE model is integrated with Incremental Dynamic Analysis (IDA), in which a representative ground-motion record is scaled across multiple intensity levels and repeated for discrete swelling states. Peak axial pipe strain is selected as the engineering demand parameter, and strain-based limit states are used to define damage states. The large ensemble of nonlinear dynamic simulations is post-processed using probabilistic regression to construct multi-hazard fragility surfaces that express damage exceedance probability as a joint function of peak ground acceleration and total swelling-induced ground heave. The results demonstrate pronounced nonlinear interaction effects, whereby swelling significantly amplifies seismic damage at low to moderate shaking intensities, behavior that cannot be captured using conventional single-hazard fragilities. The utility of the framework is demonstrated through a city-scale application for Lawton, Oklahoma, illustrating how computationally derived fragility surfaces can be embedded within spatial pipeline inventories for network-level screening. The proposed methodology provides a scalable, physics-based pathway for incorporating compound hazards into computational risk and resilience assessment of underground infrastructure systems to support network-wide screening and prioritized mitigation of the most at-risk pipeline segments.