Understanding the history of ice on Mars provides important insight into Martian geologic and climatic history. A model capable of ice reconstruction that requires few input parameters, and a detailed analyses of landforms in an area with hypothesized glacial modification, Argyre Planitia, provide further understanding of Martian ice.A threshold-sliding model was developed to model perfectly-plastic deformation of ice that is applicable to ice bodies that deform when a threshold basal shear stress is exceeded. The model requires three inputs describing bed topography, ice margins, and a function defining the threshold basal shear stress. The model was tested by reconstructing the Greenland ice sheet and then used to reconstruct ice draping impact craters on the margins of the Martian South Polar Layered Deposits using a constant basal shear stress of ~0.6 bars for the majority of Martian examples. This result is ~1/3 the value calculated for the Greenland ice sheet. Reasons for the lower Martian basal shear stress are unclear but could involve the strain-weakening behavior of ice. The threshold-sliding model can be used for ice reconstruction and forward modeling of erosion and deposition to provide further insight into the history of ice on Mars.To test the glacial hypothesis in the Argyre region, landforms are examined using images from the High Resolution Imaging Science Experiment (HiRISE) camera and other Martian datasets. Linear grooves and streamlined hills are consistent with glacial erosion. Deep semi-circular embayments in mountains resemble cirques. U-shaped valleys have stepped longitudinal profiles and tributary valleys have hanging valley morphology similar to terrestrial glacial valleys. Boulders blanketing a valley floor resemble ground moraine. Sinuous ridges cross topography, have layers, occur in troughs, and have variations in height that appear related to the surrounding surface slope; these are characteristics consistent with terrestrial eskers. At least portions of Argyre appear to be modified by ice accumulation, flow, erosion, stagnation and ablation. The type and amount of bedrock erosion and presence of possible eskers suggests the ice was, at times, wet-based.