Measurements of the dctransportcritical current of oriented‐grained YBa2Cu3O7have been made using high quality Ag contacts and a high‐current sample mount. The critical‐ current densityJcat 77 K for mutually perpendicular current and magnetic field B in thea,bplane is 8 kA/cm2at 8 T, decreasing gradually to 3.7 kA/cm2at 20 T, and remaining over 1 kA/cm2out to 30 T. High magnetic field measurements ofJcas a function of the angle &thgr; of B with respect to thecaxis are also reported. In contrast to earlier results at lower fields (<3 T) the measurements reported here in high fields reveal aJcvs &thgr; curve with ahead‐and‐shouldersshape, consisting of a sharp peak (‘‘head’’) <5° wide for B parallel to the CuO2planes, and a wide (30° at 9 T, for example) shoulder region on either side ofB⊥c, where the transportJcremains high and constant. Beyond the shoulder region, however, the transportJcdecreases sharply, giving rise to the concept of acriticalfieldanglefor application design, defined by the minima ind2Jc/d&thgr;2at the edge of the shoulders.