The present invention refers to a supply cartridge (1) comprising a package casing (11) and a support (2) of single portions, provided as a strip-like support, or similar, presenting a plurality of single dose portions (21) of an edible substance, such as for example coffee, disposed successively along a respective longitudinal direction. In particular, the cartridge (1) according to the present invention includes a support (2) of single portions adapted so that provides a more efficient and reliable movement of said support (2) of single portions out of said package casing (11).The present invention further refers to a machine (10) for preparing beverages, adapted for using a supply cartridge (1), as well as to a process of preparing beverages based upon a machine (10) for preparing beverages of the type of the present invention.