We consider the structure of Josephson vortices approaching the junction boundary with vacuum in large area Josephson junctions with the Josephson length $lambda_J$ large relative to the London penetration depth $lambda_L$. Using the stability argument for one-dimentional solitons with respect to 2D perturbations, it is shown that on the scale $lambda_J$ the Josephson vortices do not spread near the boundary in the direction of the junction. %, which is in a striking difference with behavior of Abrikosov vortices exiting superconductors. The field distribution in vacuum due to the Josephson vortex is evaluated, the information needed for the Scanning SQUID Microscopy.
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