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In this chapter the use of unstructured triangular cells for planar two-dimensional (2d) FEM models is developed. Unstructured FEM grids are bookkeeping intensive. The computer program needs three sets of information: (i) a list of nodes; (ii) a list of elements; and (iii) a list of boundary conditions. The chapter demonstrates the derivation of the coefficient matrix entries for an arbitrary triangle, before discussing data structures. It presents a simple triangular mesh (of a triangular structure) for illustrating the FEM file information and matrix assembly technique, and also a two-dimensional triangular mesh program.