The tensions produced in the wall of a rigid, thin-walled, liquid-filled sphere as it moves with an axisymmetric straining flow are examined. This problem has not been previously addressed. A generalised correlation for the maximum wall tension, expressed in dimensionless form as a Weber number (We), is developed in terms of the acceleration number (Ac) and Reynolds number (Re) of the straining flow. At low Reynolds number We is dominated by viscous forces, while inertial forces due to internal pressure gradients caused by sphere acceleration dominate at higher Re. The generalised correlation has been used to examine the case of a typical yeast cell (a thin-walled, liquid-filled sphere) passing through a typical high-pressure homogeniser (a straining-flow device). At 56 MPa homogenising pressure, a 6 mu m yeast cell experiences tensions in the inertially dominated regime (Re = 100). The correlation gives We = 0.206, corresponding to a maximum wall tension of 8 Nm(-1). This is equivalent to an applied compressive force of 150 mu N and compares favourably with the force required to break yeast cells under compressive micromanipulation (40-90 mu N). Inertial forces may therefore be an important and previously unrecognised. mechanism of microbial cell disruption during high-pressure homogenisation. Further work is required to examine the likelihood of cell deformation in the high-strain-rate short-residence-time environment of the homogeniser, and the effect that such deformation may have on the contribution of inertial forces to disruption.