This chapter describes a modeling effort to define accident prediction models for first-class main roads outside built-up areas in Hungary using variables that are available and believed to exert an influence on safety performance. Models are proposed using the Generalized Linear Modeling (GLM) approach assuming a negative binomial error structure. The chapter also overviews design characteristics and accident statistics of two-lane rural first-class main roads. Five variables are used to predict accident frequencies, Annual Average Daily Traffic (AADT), posted speed, curve, roadway width and shoulder width. Traffic volume is used as an exposure to accidents and the length of the homogenous sections. Safety Performance Functions (SPFs) have been widely used in the traffic safety field for analyzing how the safety performance of road facilities is related to various road characteristics. The chapter reviews literature to demonstrate problems associated with conventional regression techniques used for accident prediction.