In poor solvent, a flexible polymer chain (N monomers) collapses into
a globule. When stretched at both ends, it switches from a globular to
a stretched form by a first-order transition. When the coil is stretc
hed under a uniform solvent flow at velocity V, we predict that the tr
ansition is second order (continuous). We expect three regimes. (i) V
< V-1: the globule elongates slightly into an ellipsoid and the resist
ance is provided by surface tension. (ii) V-1 < V < V-2: we have coexi
stence between a reduced globule and an extended chain. (iii) Sr > V-2
: the globule has completely faded out. When stretched under a shear f
low, we also expect three regimes, but the deformation is now more pro
gressive. In the stem-globule regime, the stem can be either fully elo
ngated or only partially stretched. Finally, we discuss transients, wh
ere (i) the chain fully elongated at time t = 0 relaxes to the equilib
rium collapsed state and (ii) starting from a globule at rest, a unifo
rm flow is suddenly imposed.