A type of seismic wave, the S-wave, secondary wave, or shear wave, sometimes called an elastic S-wave, is one of the two main types of elastic body waves, so named because they move through the body of an object, unlike surface waves.

The S-wave moves as a shear or transverse wave, so motion is perpendicular to the direction of wave propagation: S-shaped, like waves in a rope, as opposed to waves moving through a slinky, the P-wave. The wave moves through elastic mediums, and the main restoring force comes from shear effects. These waves are divergenceless and obey the continuity equation for incompressible media.

$abla\; cdot\; mathbf\{u\}=0$

Its name, S for secondary, comes from the fact that it is the second direct arrival on an earthquake seismogram, after the compressional primary wave, or P-wave. Unlike the P-wave, the S-wave cannot travel through the molten outer core of the Earth, and this causes a shadow zone for S-waves opposite to where they originate. They can still appear in the solid inner core: when a P-wave strikes the boundary of molten and solid cores, called the Lehmann discontinuity, S-waves will then propagate in the solid medium. And when the S-waves hit the boundary again they will in turn create P-waves. In fact, this property allows seismologists to determine the nature of the inner core.

The velocity of an S-wave in an isotropic medium can be described by the shear modulus $mu$ and density $ho$.

$v\_s=sqrt\{frac\{mu\}\{\; ho\}\}$

As transverse waves, S-waves exhibit properties, such as polarization and birefringence, much like other transverse waves. S-waves polarized in the horizontal plane are classified as SH-waves. If polarized in the vertical plane, they are classified as SV-waves. When an S- or P-wave strikes an interface at an angle other than 90 degrees, a phenomenon known as mode conversion occurs. As described above, if the interface is between a solid and liquid, S becomes P or vice versa. However, even if the interface is between two solid media, mode conversion results. If a P-wave strikes an interface, four propagation modes may result: reflected and transmitted P and reflected and transmitted SV. Similarly, if an SV-wave strikes an interface, the same four modes occur in different proportions. The exact amplitudes of all these waves are described by the Zoeppritz equations, which in turn are solutions to the wave equation.