In this thesis we determine the submodule structure of a number of Weyl modules for algebraic groups with root systems B2 and G2. We use the Jantzen sum formula to find the composition factors of Weyl modules and go on to use homomorphisms between Weyl modules, given by H.H. Andersen, and the comparison of two filtrations of tensor products of Weyl modules to establish submodule structure. A computer program in the Prolog language is given which calculates the Jantzen sum formula. In addition we find one 2-dimensional Ext group for simple modules for type G2 in characteristic greater than or equal to 7.