  Inhomogeneous cosmological models have recently become a very interesting
alternative to standard cosmology. This is because these models are able to fit
cosmological observations without the need for dark energy. However, due to
inhomogeneity and pressure-less matter content, these models can suffer from
shell crossing singularities. These singularities occur when two shell of dust
collide with each other leading to infinite values of the density. In this
Letter we show that if inhomogeneous pressure is included then these
singularities can be prevented from occurring over the period of structure
formation. Thus, a simple incorporation of a gradient of pressure allows for
more comprehensive studies of inhomogeneous cosmological models and their
application to cosmology.
