A detailed soft x-ray survey of the Cygnus Loop, obtained from a rocket-borne experiment, provides evidence that the x-ray emission from this supernova remnant is produced by the interaction of a shock wave and the interstellar medium. A spatial map, having 0.5° by 0.5° resolution, of the structure of the Cygnus Loop in 0.2 to 1.5 kev x-rays is presented. The map shows regions of x-ray emission which correlate well with features at radio and optical wavelengths. It also shows regions for which the antithesis holds. A detailed spectral examination of the total emission from the Loop by a proportional counter equipped with a two-element filter system, shows evidence for line emission between 530 and 690 ev. The overall spectrum is found to be well represented by a thermal bremsstrahlung spectrum with line emission. The intensity of x-ray emission between 0.2 and 1.5 kev from the Cygnus Loop is found to be 1.2 ± 0.3 x 10-8 ergs/cm2-sec at the earth. Assuming a distance of 770 pc to the Loop and a columnar density of inter- stellar hydrogen of .48 ± .02 x 1021 atoms/cm2 the total energy radiated in 0.2 to 1.5 kev x-rays by the Loop is found to be 2.1 x 1036 ergs/sec. An inhomogeneous anisotropic shock wave model of the Cygnus Loop is found to be required by the data. Such a model is developed and is shown to explain the spatial and spectral appearances of the Cygnus Loop in soft x-rays. The model requires a shock front expansion velocity only as large as that implied by the optical radial velocity measurements.