The inbreeding produced during the genetic improvement of the finite populations associated to alogamous crop species is important because it is related with phenomena that are important to the breeder such as: the effective population size, the probability of the extinction of a gene, and the magnitude of the response to selection. Because of the existence of two different formulae for the inbreeding coefficient of a population associated to mass selection, a theoretical study was planned to elucidate this issue. As for the derivation of these two formulae, this study was made with a probabilistic approach, based on the ideal population model where the cycle zero (C₀) is a random sample of mn noninbred and unrelated individuals, and the random samples from cycles 1,2,3,… are formed by n families of m half sibs each. It was found that the exact inbreeding coefficient formula, derived in this study, for the cycle t (F_t) is F_t=(1+F_t-1)/(2mn)+(m-1)(1+F_t-2+6F_t-1)/(8mn)+(n-1)F_t-1/n [t=2,3,...;F₀=0 and F₁=(2mn)^-1]. For the case where C₀ is a sample of n families of m noninbred half sibs each, the inbreeding coefficients for the cycles 0 and 1 (F_0,F and F_0,F, respectively) were F_0,F=0 and F_1,F=1/(2mn)+(m-1)/(8mn); and for t = 2, 3,… the inbreeding coefficient (F_t,F) is expressable as F_t except that F_t,F is expressed in terms of F_t-1,F and F_t-2,F instead of F_t-1 and F_t-2 . To include the selection pressure effect in these two inbreeding coefficients the variance effective number N_e(V), [n(N_e(V)/m)0.5], and [(mN_e(V)/n)0.5] must substitute for mn, n, and m, respectively.