This paper is concerned with numerical solutions to the generalized coupled Sylvester matrix equations

\[ \{\begin{array}{c}\hfill {\sum }_{i=1}^{m}({A}_{1,i}X{B}_{1,i}+{C}_{1,i}Y{D}_{1,i})={E}_{1}\hfill \\\relax {\sum }_{i=1}^{m}({A}_{2,i}X{B}_{2,i}+{C}_{2,i}Y{D}_{2,i})={E}_{2}\end{array} \]

and the periodic coupled matrix equations

\[ \{\begin{array}{c}\hfill {\mathcal{A}}_{1,t}{\mathcal{X}}_{t}{\mathcal{B}}_{1,t}+{\mathcal{C}}_{1,t}{\mathcal{X}}_{t+1}{\mathcal{D}}_{1,t}+{\mathcal{E}}_{1,t}{\mathcal{Y}}_{t}{\mathcal{F}}_{1,t}={\mathcal{G}}_{1,t},\hfill \\\relax {\mathcal{A}}_{2,t}{\mathcal{X}}_{t}{\mathcal{B}}_{2,t}+{\mathcal{C}}_{2,t}{\mathcal{X}}_{t+1}{\mathcal{D}}_{2,t}+{\mathcal{E}}_{2,t}{\mathcal{Y}}_{t}{\mathcal{F}}_{2,t}={\mathcal{G}}_{2,t},\end{array}\hbox{ for }\phantom{\rule{0.25em}{0ex}}t=1,2,\dots ,\phi \]

which have many applications in several areas, such as control theory, stability theory, signal processing and perturbation analysis. By extending the bi-conjugate gradients (Bi-CG) and bi-conjugate residual (Bi-CR) methods, we obtain effective iterative algorithms for finding the solutions of the generalized coupled Sylvester and periodic coupled matrix equations. In order to compare these new algorithms with some existing methods, we present some numerical examples.