Because the inertia of tectonic plates is negligible, plate velocities result from the balance of forces acting at plate margins and along their base(1). Observations of past plate motion derived from marine magnetic anomalies provide evidence of how continental deformation may contribute to plate driving forces(2-8). A decrease in convergence rate at the inception of continental collision is expected because of the greater buoyancy of continental than oceanic lithosphere(2,3), but post-collisional rates are less well understood. Slowing of convergence has generally been attributed to the development of high topography that further resists convergent motion(7-10); however, the role of deforming continental mantle lithosphere on plate motions has not previously been considered. Here I show that the rate of India's penetration into Eurasia has decreased exponentially since their collision. The exponential decrease in convergence rate suggests that contractional strain across Tibet has been constant throughout the collision at a rate of 7.03 x 10(-16) s(-1), which matches the current rate. A constant bulk strain rate of the orogen suggests that convergent motion is resisted by constant average stress (constant force) applied to a relatively uniform layer or interface at depth. This finding follows new evidence that the mantle lithosphere beneath Tibet is intact(11), which supports the interpretation that the long-term strain history of Tibet reflects deformation of the mantle lithosphere. Under conditions of constant stress and strength, the deforming continental lithosphere creates a type of viscous resistance that affects plate motion irrespective of how topography evolved.