Urban growth implies land use changes with natural and agricultural lands becoming urbanized. Hydrological processes in these areas are significantly affected and artificial elements like channels, pipes, streets and other stormwater facilities modify the structure and connectivity of the surface drainage systems. Distributed hydrological modelling of periurban basins requires for an accurate spatial representation to take into account all these features and landscape changes. Classical approaches for terrain representation and drainage network extraction using grids do not necessarily allow considering irregular features and other elements of the complex peri-urban setting, which can also change with time. Thus, a more suitable approach to address these issues is needed. In this work we propose Geo-PUMMA, a set of GIS tools programmed in Python for GRASS that uses irregular meshes to explicitly represent the different components of the peri-urban terrain, particularly the elements affecting the flow paths (i.e. stormwater facilities, channels, streets and pipes). Geo-PUMMA gathers a series of geographical data treatment procedures which use spatial information maps (e.g. cadastral, soil types, geology and digital elevation models) to produce Hydrological Response Units (HRU) and Urban Hydrological Elements (UHEs) that make up a terrain representation more suitable for hydrologic modeling. Geo-PUMMA also allows the extraction of basin morphologic properties such as the width function, the area function and the imperviousness function, which accounts for the impervious contribution located at different distances to the outlet. Geo-Pumma is applied to 2 peri-urban catchments: the Mercier catchment (30% urbanized) located near Lyon, France, and the Estero El Guindo catchment (40% urbanized) located in the Andean piedmont in the Maipo River, Chile. Geo-PUMMA produces a terrain representation that is more representative of the actual drainage structure. Moreover, using the width function and the area function we conclude that Geo-PUMMA improves the drainage network representation particularly at small to medium spatial scales (i.e. 100-400 m for the El Guindo catchment and 50-200 m for the Mercier catchment).