Recent theoretical and experimental research on low-bulk-pinning superconducting strips has revealed striking dome-like magnetic-field distributions due to geometrical edge barriers. The observed magnetic-flux profiles differ strongly from those in strips in which bulk pinning is dominant. In this paper we theoretically describe the current and field distributions of a superconducting strip under the combined influence of both a geometrical edge barrier and bulk pinning at the strip's critical current Ic, where a longitudinal voltage first appears. We calculate Ic and find its dependence upon a perpendicular applied magnetic field Ha. The behavior is governed by a parameter p, defined as the ratio of the bulk-pinning critical current Ip to the geometrical-barrier critical current Is0. We find that when p > 2/π and Ip is field-independent, Ic vs Ha exhibits a plateau for small Ha, followed by the dependence Ic − Ip ∝ H −1 a in higher magnetic fields.The combination of a geometrical edge barrier and bulk pinning recently has been shown to strongly affect the properties of low-dimensional superconductors (thin films, single crystals, and tapes with high demagnetizing factors) placed in either a perpendicular magnetic field 1-5 or a transport-current-carrying state 6-9 . While most experimental studies of the field dependence of the critical current I c are being interpreted solely on the basis of bulk-pinning theory (see for example 10-14 ), a number of works 6,8,15,16 have shown that a geometrical edge barrier (or surface barrier) may strongly affect I c . In this paper we study the combined effect of a geometrical edge barrier and bulk pinning upon the magnetic field dependence of I c for type-II superconducting strips. We shall show how the dependence of I c upon H a is controlled by the parameter p = I p /I s0 , where I p is the bulk-pinning critical current in the absence of a geometrical edge barrier, and I s0 is the geometrical-barrier critical current in the absence of bulk pinning.We consider a superconducting strip of thickness d (|y| < d/2) and width 2W (|x| < W ) centered on the z axis. We assume that d is less than the London penetration depth λ and that W is much larger than the two-dimensional screening length Λ = 2λ 2 /d. The strip is subjected to a perpendicular applied magnetic field H a = (0, H a , 0), and it carries a total current I in the z direction described by a spatially dependent sheet current density K(x) = Jd = [0, 0, K z (x)]. We wish to determine the current-density and magnetic-field distributions at the critical current at which a steady-state flux-flow voltage appears along the length of the strip. For a strip containing no magnetic flux, K z (x) is the sum of two contributions,