This paper presents a method of changing a continuous function distributed on a element domain for boundary into a discrete function that have nodal quantities.
　The method is obtained by the use of the least squares criterion and a special differential operator matrix.
　The matrix is allowed to move out and inside integral sings even if the matrix is a differential operator. The matrix is expressed in terms of constant values associated with the element nodel co-ordinates. The conception of the method is very useful.
　This paper presents also a direct method of the finite element formulation that has physical meanings. The formulation is obtained by the use of the least squares criterion, the differential operator matrix and the Gauss' theorem. The Gauss' theorem is used to express the residuals yielding on boundaries of elementns, and the boundary residuals are formulated. Therefore, the element trial functions are not required Cm-1 continuity, and it is not necessary to integrate by parts to avoid the continuity requirement.