Method of covering non-planar surfaces of a workpiece of which at least a portion or portions are preferably of wood, engineered wood or wood-substitute materials, having the following steps: infeed of a covering material, the covering material comprising at least one weakened region, application of the covering material to at least two faces (W1-W2) of the workpiece which are, in particular, arranged at an angle to one another, the at least one weakened region being positioned in the transitional area between the at least two faces (W1-W2) of the workpiece, and in particular in the region of an inside corner, and the transitional area between the at least two faces (W1-W2) of the workpiece being so formed as to at least partly fill the weakened region of the covering material, characterised in that a connecting corner of the workpiece is covered by means of two covering materials and in particular by means of a longitudinal covering and a transverse covering, the connecting corner having a longitudinal side and a transverse side which are preferably arranged at right angles to one another, and which each have at least two faces (W1, W2, W3) of the workpiece which are, in particular, arranged at right angles to one another, and in that one of the two workpiece faces on the transverse side is identical to one of the two workpiece faces on the longitudinal side, at least one transitional area between the two faces being formed to have a bevel and/or a curved portion, and in particular a bevel at an angle of 45°, and the two covering materials (101, 102) having, on an extension of the transitional area, a complementary bevel and/or a curved portion such that they lie one on top of the other without there being any increase in height in profile. infeed of a covering material, the covering material comprising at least one weakened region, application of the covering material to at least two faces (W1-W2) of the workpiece which are, in particular, arranged at an angle to one another, the at least one weakened region being positioned in the transitional area between the at least two faces (W1-W2) of the workpiece, and in particular in the region of an inside corner, and the transitional area between the at least two faces (W1-W2) of the workpiece being so formed as to at least partly fill the weakened region of the covering material, characterised in that a connecting corner of the workpiece is covered by means of two covering materials and in particular by means of a longitudinal covering and a transverse covering, the connecting corner having a longitudinal side and a transverse side which are preferably arranged at right angles to one another, and which each have at least two faces (W1, W2, W3) of the workpiece which are, in particular, arranged at right angles to one another, and in that one of the two workpiece faces on the transverse side is identical to one of the two workpiece faces on the longitudinal side, at least one transitional area between the two faces being formed to have a bevel and/or a curved portion, and in particular a bevel at an angle of 45°, and the two covering materials (101, 102) having, on an extension of the transitional area, a complementary bevel and/or a curved portion such that they lie one on top of the other without there being any increase in height in profile.