A new method for analyzing latticed structures is presented and applied to three structural systems. The method consists of finding closed form solutions to mathematical models for structural lattices in the form of summation equations (summation-integral equations in the case of discrete-continuous systems). Two of the systems analyzed, the discrete core sandwich plate and the grid-plate structure, are examples of multidimensional lattices with multidimensional elements, a class of structural lattices that were intractable by techniques previously available. A one-dimensional lattice, the cable-supported beam, is analyzed as an introductory example. All results are numerically illustrated.