The dynamic response of a sphere in soft clay is considered through field tests in which a 0.25 m dia. steel sphere was allowed to free-fall in water and dynamically penetrate the underlying soft soil. The test data, collected in a lake and a sea environment, relate to sphere velocities of up to 8 m/s, reaching sphere invert embedments close to ten diameters. An inertial measurement unit located within the sphere measured the motion response of the sphere during free-fall and penetration in soil. The resulting acceleration data were used within a simple framework that accounts for both geotechnical shearing resistance and fluid mechanics drag resistance, but cast in terms of a single capacity factor that can be expressed in terms of the non-Newtonian Reynolds number. The merit of the framework is demonstrated by using it as a forward model in a series of inverse analyses that calculate the undrained shear strength profile from acceleration data measured in free-fall sphere tests. The good match between these profiles and those obtained from 'push-in' piezoball penetrometer tests points to the potential for an instrumented free-fall sphere to be used as a tool for characterising the near-surface strength of soft seabeds.