One embodiment of a lateral roll simulating assembly is provided which is adapted to attach to existing rowing exercise machines. It permits the user to experience various levels of physiological disequilibrium when a lack of proper balance control induces a sideways tipping action during a rowing workout. This facilitates the desirable and advantageous development of correct proprioceptive balance response using appropriate core musculature while practicing the rowing motion on a suspended rowing exercise machine. The apparatus comprises two floor-mounted members secured to each end of a rowing exercise machine that support the rowing exercise machine in a suspended condition. This assembly simulates lateral instability around the metacenter of any of a variety of rowing shells on water by allowing the rowing exercise machine to roll freely around a variety of longitudinal axes. Other embodiments are described and shown.