In this investigation, we study the monsoon variability using an ensemble of long integration (34 years) of the JMA model at T42 resolution. It was noted that a major part of the interannual variability of the Indian monsoon is by internal dynamics. Leading modes of atmospheric variability are examined using a multivariate EOF analysis. EOF-1 (obtained from a model-run with observed SST) represents the model’s response to SST variations associated with ENSO, and it has a dominant periodicity of around 4-5 years. ENSO related variability is mostly confined to the equatorial region. Over the Indian land region, the loadings of this EOF are not large. Loading associated with EOF-2 are large over the Indian region. Large-scale SST variation in the equatorial region is not seen in the spatial pattern of this mode. The rainfall pattern is characterised by positive anomalies over the Indian region, and over the central Pacific north of the equator. Rainfall anomalies of opposite sign are noticed in the warm pool regions of the western Pacific and the south-central Pacific Ocean. This EOF has a dominant periodicity on the quasi-biennial time scale (with spectral peaks at about 30 months and another at about 15 months). Spatial pattern of the EOF-1 from a climatological SST run resembles that of the EOF-2 obtained from the observed SST run and it is a natural mode of the atmospheric system. Similar analyses have been made using monthly anomalies of June to September (monsoon months). Interannual variability of rainfall has been examined using filtered rainfall anomalies during the monsoon season retaining the variability on the time scales of 15-30 months, and 36-84 months. Large rainfall variability in the climatological SST run occurs on the time scales of the QBO and ENSO as in the observed SST run. Over the Indian region, magnitudes of interannual variability in these two time scales obtained from the climatological SST run is comparable to those obtained from the observed SST run.