Our work aims at modelling and simulating the growth processes that allow the cardiovascular system to adapt to the overall body development and to changing physiological (and pathological) conditions. Within the cardiovascular system, we pay particular attention to the heart and the aorta. A healthy aortic wall succeeds in keeping a homeostatic stress level in spite of long-standing alterations in pressure or flow by triggering growth and remodelling processes that change its stress-free shape and its structure. A normal heart grows in response to the gradually increasing haemodynamic loading exerted on myocardial fibres. Postnatal cardiac growth is a form of volume-overload hypertrophy, produced essentially by a progressive myocardial cell enlargement, with no cell proliferation involved. In our continuum model, growth is basically conceived of as the time evolution of the stress-free configuration of the tiny fragments into which the modelled tissue may be subdivided in imagination. It is governed by a novel balance law—the balance of accretive couples—independent of, but constitutively coupled with, the standard balance of forces.