Thin shell structures offer a challenge to the analyst. It is well known that asymptotic expansion procedures offer simple approximate solutions for a number of shell problems for which direct numerical methods are inefficient. In this paper, a “very large finite element” method (VLFEM) is offered for the axisymmetric shell. The shape functions are obtained by sufficiently accurate asymptotic approximations through numerical procedures. A number of examples in statics and vibration have been considered that demonstrate the efficiency and accuracy of the approach.