This paper presents linear analytical and numerical studies of plasmoid instabilities in the
presence of shear flow in high-Lundquist-number plasmas. Analysis demonstrates that the
stability problem becomes essentially two dimensional as the stabilizing effects of shear flow
become more prominent. Scaling results are presented for the two-dimensional instabilities.
An approximate criterion is given for the critical aspect ratio of thin current sheets at which
the plasmoid instability is triggered.