A direct algebraic method, which can be implemented on a computer with the help of symbolic computation software like Mathematica or Maple, is used to construct a series of travelling wave solutions of two extended coupled Ito systems. The obtained solutions include solitary wave solutions, rational solutions, triangular periodic solutions, Jacobi and Weierstrass doubly periodic wave solutions. Among them, the Jacobi elliptic periodic wave solutions exactly degenerate to the solitary wave solutions at a certain limit condition. Compared with most existing tanh methods and elliptic function method, the proposed method gives new and more general solutions. More importantly, the method provides a guideline to classify the various types of the solution according to some parameters.
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