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As the undesired echo from a radar environment (clutter) is often not Rayleigh-distributed, problems arise in specifying the clutter as a non-Gaussian random process and in computer-generating realisations of clutter for simulation purposes. The paper shows that modelling the clutter as a compound Gaussian or a spherically invariant random process allows a complete specification of the clutter suitable for use in radar design. It also lends itself readily to computer simulation procedures. Specific procedures for generating clutter realisations with assigned correlation properties and with K or Weibull amplitude distributions are suggested, and are validated by statistical tests. Then the issue of resolving between the Weibull and K distributions is considered, and empirical operative characteristics of the associated hypothesis test are computed.