The structure of strong Indian monsoon low‐pressure systems (LPSs) up to forecast lead times of 15 days in 11 models of the Subseasonal‐to‐Seasonal (S2S) Prediction Project is analysed. Strong LPS (SLPS) tracks are obtained from a catalogue of LPSs tracked in all ensemble members of the S2S models during a common reforecast period of June–September 1999–2010. SLPSs, which have a minimum intensity equal to at least the upper‐quartile intensity of all LPSs, are then composited to generate horizontal and vertical structures of several dynamic and thermodynamic fields. The evolution of fields with forecast lead time and during LPS lifecycle is analysed. Furthermore, the simulation of the lower‐tropospheric monsoon circulation, precipitation biases, and the precipitation contribution of LPSs are analysed. All S2S models and the multimodel mean simulate the lower‐tropospheric monsoon circulation, but prominent dry biases are observed in the Australian Bureau of Meteorology and Environment and Climate Change Canada models. The precipitation contribution of LPSs to the summer mean precipitation is smaller in all S2S models than in tracks derived from ERA‐Interim reanalysis. The location and amplitude of the lower‐tropospheric cold core and the location of maximum precipitation are not well simulated by many models, particularly by the Hydrometeorological Centre of Russia model, in which the cold core is missing altogether. The structure of relative vorticity anomaly in all S2S models and the multimodel mean is shallower and weaker than in ERA‐Interim and MERRA‐2 reanalyses. Though the cold core intensifies through the LPS lifecycle in all models, the warm core features a midlife maximum, except in models such as Australian Bureau of Meteorology and China Meteorological Administration. These results demonstrate the potential for S2S models at simulating the structure of SLPSs, benefiting stakeholders that use S2S models for forecasting.