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Existing methodology on food accessibility predominately focuses on on-premise services, that is, dine-in and shopping at stores, which assumes a linear distance decay property (the closer, the higher accessibility). Access to delivery services is fundamentally different from that to on-premise stores. Stores with close proximity (within an inner boundary) are less desirable for delivery due to delivery fees, and there is an outer boundary beyond which deliveries are unavailable, both challenging the assumption of increasing impediment with distance. These two boundaries form a donut shape for delivery services. We propose a modified 2-step floating catchment area method that incorporates the donut shape, accounts for both demand and supply, and examines the diversity of food options. Using Seattle as a case study, our results show that delivery services increase restaurant and fast-food accessibility in areas where there is already good accessibility (e.g., downtown Seattle for restaurants and South Seattle for fast-food). Given South Seattle is where low-income and low-access households concentrate, the increase in accessibility to fast-food may not be desired. Interestingly, with delivery services, more low-income or low-access households (those who live far from grocery stores) have better accessibility to fresh produce from grocery stores compared to the rest of the population. And the newly created Supplemental Nutrition Assistance Program (SNAP) online program appears to miss low-access households. These findings have important implications for policymakers and stakeholders seeking to improve food accessibility in urban areas through delivery services.