This paper presents a technique for model reduction of spatially distributed systems. It is applicable to systems with dynamics that evolve continuously in time, but whose spatial structure is inherently discrete. The technique relies on linear matrix inequality (LMI) based synthesis results developed for control design of spatially interconnected systems. A key property which is exploited in the derivation of synthesis results is spatial invariance, which means that the system dynamics remain unchanged with translation in spatial coordinates. Such systems can be modelled by linear fractional transformations (LFTs) on spatial and temporal variables. The results in this paper are presented in terms of LMIs, making the reduction problem computationally attractive.