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The radiation mechanisms responsible for the multiwavelength emission fromrelativistic jet sources are poorly understood. The modelling of the spectralenergy distributions (SEDs) and light curves alone is not adequate todistinguish between existing models. Polarisation in the $X$-ray and$\gamma$-ray regime of these sources may provide new and unique informationabout the jet physics and radiation mechanisms. Several upcoming projects willbe able to deliver polarimetric measurements of the brightest $X$-ray sources,including active galactic nuclei (AGN) jets and $\gamma$-ray bursts (GRBs).This article describes the development of a new Monte-Carlo code -- MAPPIES(Monte-Carlo Applications for Partially Polarised Inverse External-ComptonScattering) -- for polarisation-dependent Compton scattering in relativisticjet sources. Generic results for Compton polarisation in the Thomson andKlein-Nishina regimes are presented.

Monte-Carlo Applications for Partially Polarised Inverse External-Compton Scattering (MAPPIES) -- I. Description of the code and First Results