We present an analytical model that predicts some of the mechanical effects associated with the intrusion and subsequent cooling of a rectangular intrusion emplaced at a uniform temperature into elastic continental crust. Assuming an idealized geometry and initial conditions, we recover the temperature field and subsequent strain field as a function of both position and time. The strain field is particularly relevant as it provides information on the primary (cooling-related) fracture formation pattern and direction within and immediately surrounding the pluton. We find a large strain jump across the pluton-country rock contact, implying that fracture formation should be maximized at the edges and corners of the intrusion. The direction of the fractures is predominantly vertical within the pluton centre, but becomes progressively more inclined towards the pluton margin and into the adjacent country rock. Fracture orientation may depend critically on the geometry of the intrusion, in particular the ratio of the longest to shortest dimension L1/L2.