At the article “Orthogonal curved coordinate system and forming the surfaces on trapezium plans”  there is given the method of forming of the orthogonal curved coordinate system at the plane and the methodic of forming of the new forms of the surfaces on the given trapezium curved plans. At the article there are given many pictures of the trapezium curved plans on the base of the different directrix curves and the figures of the surfaces on the given trapezium curved plans and the combinations of the surfaces with conjugated different directrix. The given methodic of the forming of the surfaces may be used in architecture and building for development of thin-walled space constructions in urban and industry building. But for calculation of stress-strain state of thin shell usually there are used the geometrical characteristics of the middle surface of the shell. At this state on the base of the vector equation of the surfaces on the trapezium curved plans there are received the formulas of the coefficients of the fundamental forms and of the curvatures of the surfaces. There are given the examples of the surfaces and there are received the formulas of the coefficients of the fundamental forms and curvatures of the surfaces with concrete directrix and functions of vertical coordinates of the surface.