It is investigated whether conditions for melting can be temporarily created in the upper sub-surface parts of snow/ice-packs on Mars at subzero surface temperatures by means of the solid-state greenhouse effect, as occurs in snow- and ice-covered regions on Earth. The conditions for this possible temporary melting are quantitatively described for bolometric albedo values A = 0.8 and A = 0.2, and with model parameters typical for the thermo-physical conditions at snow/ice sites on the surface of present Mars. It is demonstrated by numerical modelling that there are several sets of parameters which will lead to development of layers of liquid water just below the top surface of snow- and ice-packs on Mars. This at least partial liquefaction occurs repetitively (e.g. diurnally, seasonally), and can in some cases lead to liquid water persisting through the night-time in the summer season. This liquid water can form in sufficient amounts to be relevant for macroscopic physical (rheology, erosion), for chemical, and eventually also for biological processes. The creation of temporary pockets of sub-surface water by this effect requires pre-existing snow or ice cover, and thus is more likely to take place at high latitudes, since the present deposits of snow/ice can mainly be found there. Possible rheologic and related erosion consequences of the appearance of liquid sub-surface water in martian snow/ice-packs are discussed in view of current observations of recent rheologic processes.