The invention discloses an apparatus (2), a system (1) and a method (100) for characterization of vessels and for vessel modeling. The cross sectional area (A1) of the vessel is derived from pressure measurements (p1, p2) obtained by an instrument (3) from within the vessel. When multiple cross sectional areas (A1, A2) are derived for multiple reference positions (r1, r2) based on pressure measurements (p1, p2, p3) along the vessel, a representation (20, 30) of the vessel can be rendered, without requiring any imaging modality. Furthermore, the effect of the pulsatile blood flow on the elasticity of the vessel walls can be visualized, supporting assessment of a stenosis or an aneurysm formation along the vessel.