Weak gravitational lensing has become an important cosmological probe in recentyears. The deflection of light in the presence of matter is predicted from the solutionsto Einstein's equations. Observations of resulting lensing effects can be used todetermine the distribution of matter over space, allowing structure to be mapped,and constraining dark energy.In the weak lensing regime, the effects are statistical in nature and many sources arerequired. Even with a large survey area, significant systematic error may remain,arising from intrinsic alignment between galaxies. A new method, developed byresearchers at the Jodrell Bank Centre for Astrophysics, proposes to use polarisationinformation to extract the contaminating signal from intrinsic alignment.The purpose of this thesis is to model observations for weak lensing using a polarisedsky. We begin by giving an overview of the cosmological motivation, before sum-marising the lensing formalism. Finally, we develop a model of extended polarisedsources, and investigate the extraction of inputted ellipticity values from our maps.