The dependence of the fracture toughness, K(IC), on the loading rate has been calculated. On the basis of linear elastic fracture mechanics (LEFM) a strong dependence of the fracture toughness on the loading rate is obtained if subcritical crack growth is taken into account. If the subcritical crack growth parameters n and B are sufficiently small, which correspond to a high velocity of crack extension, the fracture toughness should decrease at lower loading rates. This behaviour is similar to the well-known decrease of bending strength. The experimental results for alumina containing glassy phase as a model material, however, show a maximum in a certain regime of loading rates. A model is established, which combines LEFM and the viscoelasticity, and leads to a maximum of K(IC) at a certain loading rate dependent on the viscosity of the glassy phase.