The South Asian High (SAH) is the upper-level anticyclonic-circulation over the Tibetan Plateau, strongly impacting Asian monsoon rainfall during boreal summer (June-August). The present study aims to understand the dynamic linkage between Indian summer monsoon rainfall (ISMR) and the SAH from four seasonal models (CANCM4, NEMO, CANSIP, and CFSv2). Observations indicate that the northwest-southeast (INW-SE) index of SAH is strongly correlated (similar to 0.62) with ISMR whereas the east-west (I-EW) index is negatively correlated (similar to - 0.57). All the models reasonably capture this relation between ISMR and SAH indices. The positively regressed rainfall anomalies are (90%) significant during INW-SE years and attributed to the strong cold sea surface temperature anomalies over the equatorial eastern Pacific (i.e., La Nina) and positive vorticity associated with the strong cyclonic-circulation over monsoon region. Similarly, significant negative rainfall anomalies are identified during I-EW years, strongly associated with El Nino patterns and negative vorticity anomalies over monsoon region. Unlike the CFSv2 and observations, the CANCM4, NEMO, and CANSIP models show strong positive (negative) regressed rainfall anomalies in INW-SE ((IEW)) years over India, and mainly due to strong linkage with El Nino and the Indian Ocean Dipole in the models. Overall, the high resolution CFSv2 performs better than other models for mean rainfall and teleconnections between ISMR and SAH. Of the three models, the CANCM4 performs better in capturing dynamic circulations such as vorticity, velocity potential, stream function etc. The study highlights the seasonal model's ability to capture the linkage of ISMR and SAH indices and helps understand rainfall variability.