In the general nonlinear case, fiber integrals need to be evaluated by a numerical integration technique. Several ways of going about this present themselves, each having advantages in certain circumstances.
If the integrand is a smooth function of 
, e.g. when the shell consists of one homogeneous elastic layer, then Gaussian quadrature is most efficient. For the case when the reference surface is taken to be in the middle, the one point Gauss rule only senses membrane effects. At least two points are required to manifest the bending behavior. If it is desired to include the outermost fiber points, i.e. 
, in the evaluation, then the Lobatto rules are most accurate. The two point trapezoidal rule and the three point Simpson's rule are the first two members of the Lobatto family.
In the case when the shell is built up from a series of layers of different materials such that the material properties and stresses are discontinuous function of , then Gaussian rules may be effectively used over each layer. If there are a large number of approximately equal-sized layers, then the midpoint rule on each layer should suffice. On the other hand, if there are a small number of layers or if the layers vary considerably in thickness, then different Gaussian rules should be assigned to individual layers. This is facilitated in this work by allowing the user to choose from different integration rules or input the location and weights of the fiber quadrature rule. Thus, any special set of circumstances may be accommodated.