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The term physical accessibility has widely been used by geographers, economists and urban planners and basically reflects the relative ease of access to/from several urban/rural services by considering various travelling costs. Numerous accessibility measures, ranging from simple to sophisticated, can be found in the GIS based accessibility modeling literature. However, whether simple or sophisticated, one of the fundamental shortcomings of the current GIS-based accessibility measures is that they are generally calculated from a fixed catchment area boundary based on constant traveling costs such as Euclidian (bird-flight) distance costs or transportation network-based average speed costs (e.g. 50 km/h for main streets and 30 km/h for local streets, etc.). Although such deterministic approaches are widely used in GIS-based accessibility modeling literature, they are not realistic, especially due to highly variable speeds in road segments and uncertainty in the accuracy and reliability of the accessibility measures. Therefore, this dissertation provides a new stochastic methodology for GIS-based accessibility modeling process by using GPS-based floating car data and Monte Carlo Simulation (MCS) that could handle variations in traveling costs and consider all possible catchment area boundaries, instead of one average or maximum fixed catchment area boundary. The main contribution of the research is that / the proposed physical accessibility modeling could handle uncertainties in transportation costs, create significant improvement on accuracy and reliability of accessibility measures in terms of catchment area boundaries and support decision makers who are supposed to deal with accessibility, location/allocation and service/catchment area related issues. The proposed stochastic methodology is implemented to a case study on medical emergency service accessibility, in Eskisehir, Turkey and the results of the deterministic and stochastic accessibility models are compared. The main focus of the case study is not to evaluate a specific accessibility condition in a detailed manner but to provide a methodological discussion and comparison between the deterministic and stochastic accessibility modeling process. With the implementation to a case study, it is shown that / the results of the proposed methodology are more realistic than the conventional deterministic approaches.