The India-Asia continental collision, starting at ~50 Ma, has resulted in about 2000 km crustal shortening to build the Himalaya-Tibetan plateau, which is one of the landmark terrestrial features on the Earth. In this study, using a thin viscous sheet approximation we performed scaled laboratory model experiments to investigate the spatiotemporal variation in the Himalaya-Tibetan tectonics. The experiments allow us to constrain the Tibetan plateau topography as a function of the varying India-Asia convergence rates. Our results suggest two rigid crustal blocks: Tarim and Sichuan basins steered the growth pattern in the Tibetan plateau. Because of the resistance from the rigid Tarim block western Tibet uplifted first relative to eastern part, creating a topographic elevation difference, which directed the crustal flows grossly to NE. We show from experiments the elevated plateau topography underwent gravitational collapse when the indentation velocity dropped to present average of ~3.5 cm/yr at around 18 Ma. This event eventually led to a transition from contraction to extensional tectonics, dominated by east-directed crustal flows in response to the eastward topographic gradient developed during the early stage of fast collision. We compare the present day crustal flow velocity field, strain rates, and topographic variations in the model Tibet with the actual observations in the Himalaya-Tibet Mountain System.