The starting point of this paper is the problem of fitting a polynomial to a set of unequally spaced data. Five alternative schemes which have been proposed for the solution of this problem with an automatic computer are mentioned, and the one which seems best suited to serve as a basis for a general purpose program is discussed in some detail. A practical assessment of the accuracy of the computational processes involved in this method is included. The problem in which the data are weighted is also considered, as is the problem in which constraints are imposed upon the fitting function. The procedures described for the solution of these two cases are shown to be formally equivalent. The method favoured for curve fitting is shown to possess still more advantages in solving certain types of surface fitting problems. The general problem, in which data are scattered within a finite plane area, is not discussed in this paper, which concentrates on the case, of great practical importance, in which the data are situated on parallel straight lines. The most general case considered has a “quasi-rectangular” boundary, composed of a pair of parallel sides and a pair of smooth curves. The application of constraints is again described; the procedures appropriate for curve fitting are readily generalized. A practical example of the application of the techniques for finding a constrained surface is described. Finally there is a brief review of the advantages of these procedures in common practical situations.