Pulsating strains are modelled analytically using a continuum model wi
th a well defined heterogeneous rheology. The mechanical continuum com
prises single circular cylindrical inclusions of isotropic homogeneous
viscosity hosted in a less viscous matrix. The analysis concentrates
on the behaviour of the competent inclusion and demonstrates that the
progressive deformation of the inclusion is entirely controlled by its
viscosity ratio to the host, and the orientation of the far field str
ess. The rate of deformation is determined by the stress magnitude and
the viscosity of the inclusion, but does not affect the deformation p
ath followed. An extreme case is provided by pure shear deformations w
here, by definition, the shear rate vanishes from the deformation tens
or. Vorticity will then be zero, and strains will develop coaxially wi
thout pulsation.