Summary: An extended algebraic method is devised to construct a series of complete exact solutions for some nonlinear evolution equations arising in physics. For illustration, we apply the proposed method to three nonlinear coupled physical systems, namely, the generalized Hirota-Satsuma coupled KdV system, the coupled Maccaris equations and the generalized Zakharov equations. The solutions obtained include soliton 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 soliton solutions at a certain limit condition. It is shown that the extended algebraic method provides a very effective and powerful mathematical tool for solving other nonlinear evolution equations arising in physics.