Heart muscle has a fibrous, laminar structure that influences both its mechanics and electrophysiology. Its macroscopic features can be described by a finite element model using continuous coordinate and fibre fields, and this approach is applied to modelling cardiac mechanics. Muscle contraction is brought about by the rapid spread of depolarisation throughout the tissue and to model this process requires both realistic handling of cell behaviour and detailed spatially varying fields to represent the tissue state. We discuss issues of field representation for these processes and the transformation of fields into graphical primitives for visualising models of the heart.