Collisions between bicycles and motor vehicles have caused severe life and property losses in many countries. The majority of bicycle-motor vehicle (BMV) accidents occur at intersections. In order to reduce the number of BMV accidents at intersections, a substantial understanding of the causal factors for the collisions is required. In this study, intersection BMV accidents were classified into three types based on the movements of the involved motor vehicles and bicycles. The three BMV accident classifications were through motor vehicle related collisions, left-turn motor vehicle related collisions, and right-turn motor vehicle related collisions. A methodology for estimating these BMV accident risks was developed based on probability theory. A significant difference between this proposed methodology and most current approaches is that the proposed approach explicitly relates the risk of each specific BMV accident type to its related flows. The methodology was demonstrated using a 4-year (1992-1995) data set collected from 115 signalized intersections in the Tokyo Metropolitan area. This data set contains BMV accident data, bicycle flow data, motor vehicle flow data, traffic control data, and geometric data for each intersection approach. For each BMV risk model, an independent explanatory variable set was chosen according to the characteristics of the accident type. Three negative binomial regression models (one corresponding to each BMV accident type) were estimated using the maximum likelihood method. The coefficient value and its significance level were estimated for each selected variable. The negative binomial dispersion parameters for all the three models were significant at 0.01 levels. This supported the choice of the negative binomial regression over the Poisson regression for the quantitative analyses in this study.