The problem of accommodation of constrained deformation by slip and twinning has been analysed. The analysis is based on Taylor's least work hypothesis. In this analysis, the operative combination of slip and twinning systems is found by minimizing the orientation factor M = ($\Sigma_i$s$_i$ + $\alpha \Sigma_i$t$_i$)/$\epsilon$, where s$_i$ and t$_i$ are the simple shears resulting from slip and twinning respectively, $\alpha$ is the ratio of the critical resolved shear stress for twinning against slip, and $\epsilon$ is the external strain. Detailed calculations have been made for face-centred cubic crystals deformed by plane strain compression. Experimental observations on deformed single crystals of a Co-8% Fe alloy indicate good agreement with the analysis. Implications of the present study to the twinning observations of Heye & Wassermann on rolled Ag crystals are discussed.