Accessibility models in transport geography based on geographic information systems have proven to be an effective method in determining spatial inequalities associated with public health. This work aims to model the spatial accessibility from populated areas within the Concepción metropolitan area (CMA), the second largest city in Chile. The city's public hospital network is taken into consideration with special reference to socio-regional inequalities. The use of geographically weighted regression (GWR) and ordinary least squares (OLS) for modelling accessibility with socioeconomic and transport variables is proposed. The explanatory variables investigated are: illiterate population, rural housing, alternative housing, homes with a motorised vehicle, public transport routes, and connectivity. Our results identify that approximately 4.1% of the population have unfavourable or very unfavourable accessibility to public hospitals, which correspond to rural areas located south of CMA. Application of a local GWR model (0.87 R2 adjusted) helped to improve the settings over the use of traditional OLS methods (multiple regression) (0.67 R2 adjusted) and to find the spatial distribution of both coefficients of the explanatory variables, demonstrating the local significance of the model. Thus, accessibility studies have enormous potential to contribute to the development of public health and transport policies in turn to achieve equality in spatial accessibility to specialised health care.