The elastic model assumes that changing the momentum of the liquid causes expansion or compression of the pipeline and liquid, both assumed to be linear-elastic. Since the liquid is not completely incompressible, its density can change slightly during the propagation of a transient pressure wave. The transient pressure wave will have a finite velocity that depends on the elasticity of the pipeline and of the liquid as described in Celerity and Pipe Elasticity.

In 1898, Joukowski established a theoretical relationship between pressure and velocity change during a transient flow condition. In 1902, Allievi independently developed a similar elastic relation and applied it to a uniform valve closure. The elastic theory developed by these two pioneers is fundamental to the field of hydraulic transients. The combined elasticity of both the water and the pipe walls is characterized by the pressure wave speed, a. This relation is a simplified form of the equation (see equation ) applicable to an instantaneous stoppage of velocity.

(H - H_o) = -a / g (V - V_o)

For an instantaneous valve closure or stoppage of flow, the upsurge pressure (H-H _o ) is known as the "Joukowski head." Given that a is roughly 100 times as large as g, a 1 ft./sec. (0.3 m/s) change in velocity can result in a 100 ft. (30 m) change in head. Because changes in velocity of several feet or meters per second can occur when a pump shuts off or a hydrant or valve is closed, it is easy to see how large transients can occur readily in water systems.

The mass of fluid that enters the part of the system located upstream of the valve immediately after its sudden closure is accommodated through the expansion of the pipeline due to its elasticity and through slight changes in fluid density due to its compressibility. This equation does not strictly apply to the drop in pressure downstream of the valve, if the valve discharges flow to the atmosphere.