Precise actuation of continuum surfaces in combination with continuum robotic arms that undergo large deformation is of high interest in soft robotics but of limited model-based study to date. This work develops this area towards enabling the robust design and control of large deformation continuum surfaces (LDCS) across multiple industrial applications in the healthcare, aerospace, manufacturing, and automotive domains. It introduces an actuation based dynamic model of LDCSs to accurately determine their deflection due to application of concentrated external forces while maintaining many physical characteristics and constraints on actuation elements and surface structure such as gravity, inertia, damping, elasticity, and interactive forces between actuators and LDCS. Using the lumped-mass methodology, a 3D integrated surface-arm model is developed, simulated and then validated experimentally where a pair of parallel arms are attached to the surface to actuate and deform it. The surface is then simultaneously subjected to a concentrated constant external force at its top center between the two arms. Comparing measured displacements between the experimental and modelling results over actuation time yielded the maximum error is less than 1% of the length of the surface's side at its final deflected profile despite the limited number of nodes (masses) used in the LDCS model while it is exposed to a significant external force.