This paper presents a collisional model for asteroids and their debris in the asteroidal belt. The model describes the evolution of a system of particles undergoing inelastic collisions and fragmentation, leading to a steady-state distribution. An integro-differential equation is derived to describe the time rate of change of the number density of particles in a given mass range due to erosion, catastrophic collisions, and particle creation through collisional fragmentation. The solution to this equation is found to be a power law function, with the population index α = 1.837, which is consistent with empirical observations of asteroidal debris. The model is applied to estimate the number density and statistical properties of debris in the asteroidal belt. It is found that catastrophic collisions are the primary physical process determining particle lifetimes and the form of the particle distribution for particles large enough that radiation effects are negligible. The lifetime of the largest asteroids is comparable to the probable lifetime of the solar system, suggesting that some of the largest asteroids may have survived since the early formation of the solar system, while most smaller ones are collisional fragments. The paper also discusses the observational evidence for the distribution of known asteroids, including their statistical properties, and compares these with the theoretical predictions of the model. The results show that the theoretical population index α = 1.837 is within the margin of error of the empirical fit to the observed asteroid catalog. The model distribution is normalized to the observed number of asteroids, providing a basis for further analysis and comparison with other data.This paper presents a collisional model for asteroids and their debris in the asteroidal belt. The model describes the evolution of a system of particles undergoing inelastic collisions and fragmentation, leading to a steady-state distribution. An integro-differential equation is derived to describe the time rate of change of the number density of particles in a given mass range due to erosion, catastrophic collisions, and particle creation through collisional fragmentation. The solution to this equation is found to be a power law function, with the population index α = 1.837, which is consistent with empirical observations of asteroidal debris. The model is applied to estimate the number density and statistical properties of debris in the asteroidal belt. It is found that catastrophic collisions are the primary physical process determining particle lifetimes and the form of the particle distribution for particles large enough that radiation effects are negligible. The lifetime of the largest asteroids is comparable to the probable lifetime of the solar system, suggesting that some of the largest asteroids may have survived since the early formation of the solar system, while most smaller ones are collisional fragments. The paper also discusses the observational evidence for the distribution of known asteroids, including their statistical properties, and compares these with the theoretical predictions of the model. The results show that the theoretical population index α = 1.837 is within the margin of error of the empirical fit to the observed asteroid catalog. The model distribution is normalized to the observed number of asteroids, providing a basis for further analysis and comparison with other data.