Apatite fission-track thermochronology has been based upon measurements in prismatic sections. Until now, all annealing data sets referred to this kind of measurement. However, prismatic sections are not always available, e.g. for detrital apatite grains, making the work impossible. An alternative would be to use grains in any orientation. This requires that a suitable annealing model be employed, i.e. one obtained from measurements in grains without preferential orientation. In this work, the angular distribution of confined fission tracks parallel to the surfaces of grains randomly oriented relative to the crystallographic c-axis is obtained. This distribution shows that track at higher angles relative to c-axis, when compared with the prismatic section distribution, are found. The procedure measurements in randomly oriented sections is presented along with empirical model equations. Model parameters have been obtained for the most common empirical equations and the partial annealing zone has been calculated for these equations. Results are compared with geological benchmarks; the fanning linear Arrhenius model yields the best agreement. This empirical model and those most used in literature have been applied to samples from the São Francisco Craton, Brazil, to show an instance in which the effects of grain orientation is important. Thermal histories of geological samples have been obtained through these equations. The samples tested presented moderate annealing and experienced a relatively simple thermal history. Under these conditions, taking into account the uncertainties in the model equations and confined track measurements, and using compatible systems, the presented model equations and the most used prismatic face ones constrained the same thermal history feature. © 2007 Elsevier B.V. All rights reserved.