Abstract Deformation systems (DSs) locally affect the South Polar Layered Deposits (SPLDs) along the margins of the Promethei Lingula ice sheet (part of the southern Martian ice-dome). One example is the ‘S 2 ’ deformation system, characterized by a complex pattern of brittle and brittle–ductile structures related to kilometre-scale shear zones that deform the sequence. Moreover, soft-sediment structures affect one layer located at the base of the S 2 . An earlier structural analysis suggested that: (1) two deformation stages (D 1 , in which the shear zones developed, and D 2 , in which the D 1 structures were reactivated by deep-seated gravitational slope deformation) occurred, driven by gravity; and (2) there are variations in the bulk composition of the SPLD (which is inferred to be mainly composed of water ice plus basaltic dust). This work supports these structural results through thermal and mechanical modelling of the S 2 sequence. Our modelling results suggest that several layers within the S 2 system are probably composed of, or are mixed with, CO 2 ice, and that the development of the observed deformation is inconsistent with present-day physical conditions. Soft-sediment structures probably formed under warmer surface temperatures during the past, with those warmer temperatures favouring or even triggering ice flow/basal sliding of the Promethei Lingula. Supplementary material: The complete description of the stratigraphy of the analysed S 2 sequence (in table format) is available at http://www.geolsoc.org.uk/SUP18746 .