Abstract: With the aid of Hormander's method, a set of partial differential equations governing orthotropic shallow shells involving transverse shear deformation is reduced into a tenth order partial differential equation with one function as unknown.By the use of the method of plane wave decomposition, this partial differential equation is transformed into an ordinary differential equation.The fundamental solutions for the orthotropic shallow shells are presented in the form of a definite integral.The calculation of the fundamental solutions is discussed in detail.