Dust grains play an important role in determining the cooling, the
 thermal structure, and the abundance of various refractory elements in
 fast astrophysical shocks (see review by Dwek & Arendt 1992). Equally
 important is their destruction, which recycles condensible elements
 from the solid back to the gaseous phase of the interstellar medium
 (ISM). On a galactic scale, grain destruction regulates the depletions
 of various refractory elements in the interstellar medium and on a
 local scale, it affects the ionization structure of the shock,  as well
 as the infrared (IR), the ultraviolet (UV), and the X-ray signature of
 the shocked gas. There is, however, only circumstantial evidence for
 the destruction of grains in fast shocks, mostly inferred from IRAS
 observations of young supernova remnants. Sputtering changes the
 initial grain size distribution, depleting the population of small
 grains. These small dust particles with sizes below 0.03 microns are
 stochastically heated, undergo temperature fluctuations, and radiate an
 excess of near infrared emission (lamda<30 um) over that expected for
 grains in thermal equilibrium. This near infrared excess is a measure
 of the abundance of small grains, and therefore a powerful diagnostic
 for the amount of destruction the grains concurred in the shock. The
 ISO satellite offers unique capabilities for obtaining the short
 wavelength emission from stochastically-heated dust in SNRs. We propose
 to use ISOPHOT to observe emission from dust both inside and outside
 several SNR shock fronts over a very broad range of wavelengths.