Intermediate filaments are a key component of the cytoskeleton. Their transport along microtubules plays an essential role in the control of the shape and structural organization of cells. To identify the key parameters responsible for the control of intermediate filament transport, we generated a model of elastic filament transport by microtubule-associated dynein and kinesin. The model is also applicable to the transport of any elastically-coupled cargoes. We investigate the effect of filament properties such as number of motor binding sites, length, and elasticity on motion of filaments. Additionally, we consider the effect of motor properties, i.e. off rates, on filament transport. When one motor has a catch bond off rate it dictates the motion, whereas when motors have the same type of off rate filaments can alternate between retrograde and anterograde motions. The elasticity of filaments optimizes the filament transport and the coordination of motors along the length of the filament.