Observations of volcanoes extruding andesitic lava to produce lava domes often reveal cyclic behaviour. At Soufriere Hills Volcano, Montserrat, cycles with sub-daily and multi-week periods have been recognised on many occasions. These two types of cycle have been modelled separately as stick-slip magma flow at the junction between a dyke and an overlying cylindrical conduit (Costa et al. 2012), and as the filling and discharge of magma through the elastic-walled dyke (Costa et al., 2007a) respectively. Here, we couple these two models to simulate the behaviour over a period of well-observed multi-week cycles, with accompanying sub-daily cycles, from 13 May to 21 September 1997. The coupled model captures well the asymmetrical first-order behaviour: the first 40% of the multi-week cycle consists of high rates of lava extrusion during short period/high amplitude sub-daily cycles as the dyke reservoir discharges itself. The remainder of the cycle involves increasing pressurization as more magma is stored, and extrusion rate falls, followed by a gradual increase in the period of the sub-daily cycles