The interaction of supernova blast waves with the inhomegenous interstellar medium leads to a wide variety of morphologies for middle-aged supernova remnants. For many remnants, the expected shell morphology is missing the X-ray and/or radio, and the X-rays may be center-filled while the optical morphology is a partial shell. It has been speculated that some of the unusual morphologies are due to interaction with denser regions in the interstellar medium. Because the cooling rate is much higher in dense regions, the shock rapidly becomes radiative and X-rays would be absent. One of the main coolants is the OI 63-micron line, which can be observed with unprecedented sensitivity by ISO. We propose observtaions of 8 SNR (W 28, W 44, CTB 109, IC 443, Puppis A, PKS1209-52, 3C391, and Kes 79) that are suspected or known to be interacting with dense clouds, and also have been imaged in X-rays by ROSAT or ASCA. The goals of our observations are (1) to detect the OI line, which will provide definite evidence for interaction, even where searches for broad CO lines have failed; (2) to compare the X-ray and OI cooling rates, which will distinguish where the shock has become radiative; and (3) to determinine the distribution of OI emission, which will provide insight into the role of the inhomogenous interstellar medium in the evolution and morphology of SNR.