Despite significant research on spallation, there are still unexplored gaps such as the spall fracture delay. In this case, fracture occurs not at the growth stage of tensile stress in a spall section but at the stage of stress stabilization or reduction. However, no attention was paid to this effect. In this paper, we present an experimental and theoretical study to verify the existence of the delay effect. The experiments were carried out on steel specimens under the action of threshold and overloaded impulses. It was found that the spall fracture delay can be realized at the threshold fracture impulses. In order to calculate the fracture stress, the stress history should be considered correctly. For this purpose, the incubation time approach was employed. The incubation time criterion allowed calculating the stress rate dependence of fracture stress and time to fracture taking into account the spall fracture delay at threshold impulses. The calculated curves are in good agreement with the experimental points.