Mechanical stretch plays a major role in modulating atrial function, being responsible for beat-by-beat responses to changes in chamber preload, enabling a prompt regulation of cardiac function. Mechano-electric coupling (MEC) operates through many mechanisms and has many targets, making it experimentally difficult to isolate causes and effects especially under sinus conditions where effects are more transient and subtle. Therefore, modelling is a powerful tool to help understand the role of MEC with respect to the atrial electromechanical interaction. We propose a cellular-based computational model of the left atrium that includes a strongly coupled MEC component and mitral flow component to account for correct pressure generation in the atrial chamber as a consequence of blood volume and contraction. The method was applied to a healthy porcine left atrium. Results of the strongly coupled simulation show that strains are higher in the areas adjacent to the mitral annulus, the rim of the appendage, around the pulmonary venous trunks and at the location of the Bachmann's bundle, approximately between the mitral annulus and the region where the venous tissue transitions into atrial. These are regions where arrhythmias are likely to originate. The role of stretch-activated channels was very small for sinus rhythm for the single cardiac beat simulation, although tension development was very sensitive to stretch. The method could be applied to investigate potential therapeutic interventions acting on the mechano-electrical properties of the left atrium.