We present measurements of critical currents and critical magnetic fields in cylindrical indium films. The most interesting result is that the ratio of the experimental critical current I(c1) to Silsbee's critical value I(c0) practically does not depend on temperature. This ratio was strongly dependent on the film thickness changing from I(c1) almost-equal-to 0.18I(c0) for the film thickness d = 0.3 mum to I(c1) almost-equal-to 1.3I(c0) for d = 5.5 mum. These results cannot be explained in the framework of the existing theoretical models.