Long‐term records of the flow patterns and dynamics of surge‐type glaciers improve our understanding of their underlying dynamic processes, and are critical to better resolve their contribution to a changing cryosphere. We adapt a modeling approach designed to emulate glacier surging and fold kinematics using the full Stokes ice‐flow model Elmer/Ice to simulate surging of the Dusty Glacier, located in the St. Elias Mountains, Canada. We combine distributed mass‐balance and numerical ice‐flow models to reconstruct the fold kinematics of the 2001–2003 surge of the Dusty Glacier by comparing model results to Landsat‐7 and Sentinel‐2 imagery, and assess the sensitivity of centennial‐scale modeled glacier structure to different mass balance and sliding parameterizations. This study demonstrates the feasibility of using the approach to reconstruct the surface structure kinematics of a surge‐type glacier in nature, highlighting its potential application to other surge‐type glaciers and regions. Plain Language Summary Glaciers can exhibit irregular flow patterns that complicate predictions of their evolution over the coming decades and centuries. We present a method for reproducing iconic surface structures known as folded medial moraines using glaciological modeling. These moraines are wavy flow patterns found on surge‐type glaciers, highlighted by sediment deposited onto the ice that traces their path. By reconstructing these patterns, the underlying climate and sliding conditions that contributed to the glacier's past flow can be identified. Improving our knowledge of these conditions can help improve glacier flow models. We demonstrate that our methodology successfully reconstructs the flow patterns present on a large surge‐type glacier in Yukon, Canada, and explore its past flow history, and possible future, based on these results. Key Points We use a distributed mass‐balance model and Elmer/Ice to reconstruct the 2001–2003 surge kinematics of the Dusty Glacier, Yukon, Canada We explore the centennial‐scale sensitivity of glacier surface fold geometry to mass balance and sliding parameterizations This study is a proof‐of‐concept for further model reconstructions of the past dynamics of surge‐type glaciers