The effects of velocity skewness on the oscillating Stokes layer are investigated. Linear stability characteristics for the family of velocity-skewed time-periodic flows are determined using Floquet theory. Neutral stability curves and critical parameter settings for instability and the structure of the eigenfunctions are presented. Velocity skewness establishes a stabilizing effect and increases the critical Reynolds number for the onset of linear instability to larger values than that found in the non-skewed Stokes layer. Solutions indicate that disturbances develop in the direction that the wall velocity achieves a maximum absolute value.