Gravitational lens modelling of spatially resolved sources is a challenging inverse problem that can involve many observational constraints and model parameters. Existing methods use a Bayesian framework to reconstruct the source on a possibly irregular or adaptive grid, while imposing reasonable priors on the source's surface brightness distribution. We present a new method of reconstructing the lensed source that reduces the number of free parameters and increases computational efficiency. Instead of reconstructing the source on a grid, the source's surface brightness is described analytically using a limited subset of a complete and orthonormal set of basis functions, known as shapelets, and priors on the source can also be enforced using the shapelets in a grid-free way. Finally, we show how the shapelets framework fits into existing Bayesian frameworks for strong lens modelling and how it can be extended to the visibility space for modelling interferometric data.