Seabed strength may be determined rapidly using free-fall penetrometers as the tool is simply released from above the sea-floor and penetrates under gravity into the seabed. The speed and ease of deployment relative to conventional ‘push-in’ penetrometers is attractive, with the trade-off of more complex interpretation. This paper considers two approaches for deducing the undrained shear strength from a slender conical tipped penetrometer. The first requires as input only the vertical acceleration of the penetrometer, where the soil strength is determined indirectly by considering the various forces acting on the penetrometer and solving the equation of motion. The second determines the undrained shear strength more directly by combining tip load cell and u2 pore pressure measurements. In both cases, adjustments for drag resistance and strain-rate effects are necessary to deduce a strength compatible with that determined from the equivalent push-in penetrometer test. Application of both methods to a series of centrifuge tests in normally consolidated kaolin clay reveals that the direct method – using the tip load cell and u2 pore pressure measurements – is much more reliable and can produce strength profiles that are within 10% of those obtained from push-in piezocone tests, compared with variations of up to 75% for the indirect accelerometer based method, which requires additional assumptions. The centrifuge study also provides direct quantification of the strain rate enhancement of tip and shaft resistance, revealing much higher strain rate dependency for shaft resistance than is typically allowed for.