Non‐technical summary  The heartbeat depends on the spread of electrical waves through the cardiac muscle. If that spread becomes disturbed, arrhythmias and death may ensue. Patients with heart disease are predisposed to cardiac arrhythmias by unidentified mechanisms. Using both experiments and computer models we demonstrate that structural defects in the heart leading to contiguous areas of physical narrowing and expansion of the musculature can alter the spread of the waves, in such a way that some waves may return abnormally along the same narrow pathway as the original electrical wave (reflection), leading to extra beats and arrhythmia initiation. The possibility of reflection is enhanced when structural defects combine with alterations in the sodium channels responsible for the electrical waves, such as seen in inherited and acquired cardiac electrical diseases. Our results provide a novel mechanism whereby a substrate (structural heterogeneity) and a trigger (abnormal sodium channel activity) combine to promote life‐threatening arrhythmia initiation.