A method of evaluating a tetrahedral linear interpolation function utilizes a table preparation process and a linear interpolating process. In the table preparation process, values v and domain points p of the function are related by two tetrahedral interpolation variables denoted as a matrix T and a vector t, as follows: v=t+pT. The coordinates of p include n components, and the value v includes m components. The matrix T includes n rows and m columns, as it must to relate p to v. If the value of the function is scalar, t is also a scalar, and T is a vector of n elements. From the coordinates of the (n+1) domain input points and the function values v at these points, the values of variables t and T are computed and stored in a table. The linear interpolation procedure of the invention uses the values tabulated for t and T to calculate an approximation for the components of the function value v at a given p. The function arguments are stored in a first array of n elements denoted as p[i], and the calculated approximations are to be stored in a second array of m elements denoted as v[j]. The approximations for the array v[j] may be calculated according to the following equation: ##EQU1##