A response of a swept wing boundary layer to a single free-stream stationary axial vortex of a limited spanwise extent is investigated. The response is dominated by streamwise velocity perturbations that grew quasi-exponentially downstream. It is shown that the formation of the boundary layer disturbance occurs for the most part close to the leading edge. The disturbance represents itself a wave packet consisted of the waves with characteristics specific for cross-flow instability. However, an admixture of growing disturbances which origin can be attributed to transient effects and distributed receptivity mechanism is also identified.