Northern peatlands appear to hold large volumes of free‐phase gas (e.g., CH₄ and CO₂), which has been detected by surface deformations, pore pressure profiles, and electromagnetic surveys. Determining the gas content and its impact in peat is challenging because gas storage depends on both the elastic properties of the peat matrix and the buoyant forces exerted by pore fluids. We therefore used a viscoelastic deformation model to estimate these variables by adjusting model runs to reproduce observed changes in peat surface elevation within a 1300 km² peatland. A local GPS network documented significant changes in surface elevations throughout the year with the greatest vertical displacements associated with rapid changes in peat water content and unloadings due to melting of the winter snowpack. These changes were coherent with changes in water table elevation and also abnormal pore pressure changes measured by nests of instrumented piezometers. The deformation model reproduced these changes when the gas content was adjusted to 10% of peat volume, and Young's modulus was varied between 5 and 100 kPa as the peat profile shifted from tension to compression. In contrast, the model predicted little peat deformation when the gas content was 3% or lower. These model simulations are consistent with previous estimates of gas volume in northern peatlands and suggest an upper limit of gas storage controlled by the elastic moduli of the peat fabric.