The ARIES team is currently proposing two tungsten divertor concepts for its tokamak designs and has performed extensive analyses to optimize their thermal and structural performance. Because of the high divertor operating temperatures and the low ductility of tungsten, thermal creep and fracture will be important failure mechanisms to consider. This paper presents a series of finite element analyses addressing the viable operating ranges of these tungsten plate divertor concepts with respect to creep and fracture. For fracture, the J-integral, a path-independent contour integral that estimates the strain energy release rate for a crack of assumed geometry, is used to address crack propagation. Elliptical surface cracks are introduced both inside and outside the coolant channel, and steady-state calculations are carried out for both full-power and cold shutdown conditions. It is determined that the critical crack is on the inside of the coolant channel with the highest stress intensities at full-power operation. Also, transient creep simulations are performed to predict the high-temperature thermal deformations and creep strains at various surface flux levels. Finally, transient thermal calculations are carried out to simulate edge-localized modes in the plasma, and conclusions are drawn with respect to the severity and frequency of these events with respect to surface melting for the two concepts.