A numerical model was developed for the time-dependent thermal behaviour of walls with significant thermal inertia exposed to varying meteorological conditions. Walls with sufficiently large heat storage capacity may absorb a significant proportion of the heat entering a building from external sources, so reducing, broadening and delaying the peak temperature experienced internally. This reduces demands on air conditioning equipment. Lightweight panel, composite concrete, and composite brick walls were modelled using a finite difference technique to predict transient and quasi-steady-state thermal behaviour. The reduction of the daily fluctuation in the quasi-steady-state heat flux was quantified using a dimensionless number termed the wall damping-out efficiency. The model predictions were in agreement with literature data. Calculations for a mild Mediterranean climate indicated that brick walls were superior to concrete during winter, and exhibited slightly better performance during the summer. 14 refs.