  Dependence of the critical current $I_c$ on the applied magnetic field $H_a$
is theoretically studied for a thin superconducting strip of a rectangular
cross section, taking an interplay between the Bean-Livingston and the
geometric barriers in the sample into account. It is assumed that bulk vortex
pinning is negligible, and the London penetration depth $\lambda$ is
essentially less than the thickness $d$ of the strip. To investigate the effect
of these barriers on $I_c$ rigorously, a two-dimensional distribution of the
current over the cross section of the sample is derived, using the approach
based on the methods of conformal mappings. With this distribution, the
dependence $I_c(H_a)$ is calculated for the fields $H_a$ not exceeding the
lower critical field. This calculation reveals that the following two
situations are possible: i) The critical current $I_c(H_a)$ is determined by
the Bean-Livingston barrier in the corners of the strip. ii) The geometrical
barrier prevails at low $H_a$, but with increasing magnetic field, the
Bean-Livingston barrier begins to dominate. The realization of one or the other
of these two situations is determined by the ratio $\lambda/d$.
