A mathematical model was developed to calculate the dose to equipment inside containment of power reactors following a maximum hypothetical accident (MHA). The model permitted both instantaneous and time-dependent releases and incorporated decay chains up to six isotopes in length. The release of noble gases produced by the decay of halogens that plate out on surfaces or are trapped by filters was taken into account. The resulting equations were solved analytically. The gamma and beta dose due to an MHA from a 3-GW(th) reactor was computed using this model. Results show that the use of decay chains produces a 38% increase in dose, and an instantaneous release produces a dose that is 14% higher than the time-dependent release.