Strength interpretation from the measured penetration resistance of full-flow penetrometers, such as the T-bar and ball, is generally based on a constant bearing capacity factor associated with a deep flow-round mechanism. This approach may underestimate the strength of near-surface sediments, which is becoming increasingly important for the design of offshore infrastructure such as pipelines, steel catenary risers and mudmats. This paper describes a series of centrifuge experiments designed to capture the change in the capacity factor of a ball penetrometer during shallow penetration. A rigorous consideration of soil buoyancy is provided. This is an important consideration in soils with a higher strength to self-weight ratio because a cavity is formed by the passage of the ball and remains open to greater depths. The depth at which a full-flow mechanism develops is related to the dimensionless strength ratio, expressed as the ratio of the undrained shear strength to the effective unit weight and penetrometer diameter. This observation forms the basis for proposed formulations that describe the evolution of the bearing capacity factor with depth for different dimensionless strength ratios. These formulations can be used to determine more accurately the undrained shear strength of near-surface soil over the range of dimensionless strength ratios that is of interest to offshore applications.