The aim of this paper is to measure the spatial accessibility to public health care facilities in Greece. We look at population groups disaggregated by age and socioeconomic characteristics. The purpose of the analysis is to identify potential spatial inequalities in the accessibility to public hospitals among population groups or service areas. The data refer to the accessibility of all residents to public hospitals in Greece. The spatial datasets include the location of settlements (communities), the administrative boundaries of municipalities and the location of public hospitals. The methodology stems from spatial analysis theory (gravity models), economics theory (inequalities) and geocomputation practice (GIS and programming). Several accessibility measures have been calculated using the newly developed R package <i>SpatialAcc</i>, which is available in CRAN. The results are interesting and tend to show an urban-rural and social class divide: younger, working age population as well as people with the highest educational attainment have better accessibility to public hospitals compared to older or low educated residents. This finding has serious policy making implications and should be taken into account in the future spatial (re)organisation of hospitals in Greece.