Three planets with minimum masses less than 10 M⊕ orbit the star HD 40307, suggesting these planets may be rocky. However, with only radial velocity data, it is impossible to determine if these planets are rocky or gaseous. Here we exploit various dynamical features of the system in order to assess the physical properties of the planets. Observations allow for circular orbits, but a numerical integration shows that the eccentricities must be at least 10–4. Also, planets b and c are so close to the star that tidal effects are significant. If planet b has tidal parameters similar to the terrestrial planets in the solar system and a remnant eccentricity larger than 10–3, then, going back in time, the system would have been unstable within the lifetime of the star (which we estimate to be 6.1 ± 1.6 Gyr). Moreover, if the eccentricities are that large and the inner planet is rocky, then its tidal heating may be an order of magnitude greater than extremely volcanic Io, on a per unit surface area basis. If planet b is not terrestrial, e.g., Neptune-like, these physical constraints would not apply. This analysis suggests the planets are not terrestrial-like, and are more like our giant planets. In either case, we find that the planets probably formed at larger radii and migrated early-on (via disk interactions) into their current orbits. This study demonstrates how the orbital and dynamical properties of exoplanet systems may be used to constrain the planets' physical properties.