Because of the full covariance matrices and the computer storage limitations the number of measurements which can be handled by the collocation method simultaneously, is limited. This paper presents a method to compute covariance functions with a finite support yielding sparse covariance matrices. The theoretical background is pointed out and, for the one- and two-dimensional case, special functions are developed which can be combined with the usually used covariance functions to get a “finite covariance function”. Simulated examples to demonstrate the behaviour of different solution methods to solve these special, sparse covariance matrices supplement our investigations.