Food accessibility has been a subject of growing interest due to its impact on public health outcomes. This paper describes a spatial analysis method to identify gaps in geographic food access and correlate them with a variety of demographic and socioeconomic factors. The proposed food accessibility metric is the square footage of supermarkets that can be reached within 10 min travel time by walking, biking, driving, and 30 min travel time by walk/transit. The spatial analysis is conducted for the centroids of each census tract within a study area, and the approach is illustrated with an application for the state of Massachusetts. Correlations between demographic and socioeconomic explanatory variables and food accessibility are explored using the Gradient Boosted machine learning model. More specifically, the explanatory variables are percent minority population, percent of population in poverty, vehicle ownership, and population density. The spatial analysis shows a strong correlation between food accessibility and population density. The machine learning model is then used to identify gaps in food accessibility for each transportation mode while controlling for community characteristics. The residuals of the model reveal which communities have the lowest food accessibility relative to other similar communities within the state. This research provides a quantitative method to identify communities that have reduced access to food relative to state-wide trends. Lastly, it provides insights for where policy interventions would be valuable for improving food access in addition to recommendations on increasing food accessibility.