A surface covering kit, comprising: a plurality of rectangular panels, each panel defining a panel plane and each panel having an upper and a lower panel surface in parallel to the panel plane and two parallel, opposing longitudinal sides (104, 104') and two parallel, opposing transverse sides (105, 105'), the transverse sides (105, 105') being provided with grooves (301, 302, 301', 302') adapted to form an insertion channel when two panels are laid next to each other along their transverse sides (105, 105') in a common laying plane; and at least one extraneous locking element adapted to be received by said insertion channel along an insertion direction in parallel to the transverse side to lock two adjacent panels to each other relative to a first direction parallel to their common laying plane and perpendicular to the transverse sides (105, 105') as well as relative to a second direction perpendicular to their common laying plane, the extraneous locking element having a longitudinal dimension and a cross-section perpendicular to said longitudinal dimension which substantially forms a cross with at least four cross arms (901, 902, 903, 904),), wherein said grooves (301, 302, 301', 302') are oriented in such a manner that each of the cross arms (901, 902, 903, 904) is oriented diagonally between said first and said second directions when said extraneous locking element is received by said insertion channel, characterized in that a compensation groove (305, 306) extending substantially in parallel to the transverse sides (105, 105') with two substantially parallel flanks is provided between two adjacent panels when said panels are laid next to each other along their transverse sides (105, 105') in a common laying plane, such that a lower part of the compensation groove extends all the way from the insertion channel to the lower panel surface, and an upper part of the compensation groove extends from the insertion channel upwards at most partially towards the upper panel surface. a plurality of rectangular panels, each panel defining a panel plane and each panel having an upper and a lower panel surface in parallel to the panel plane and two parallel, opposing longitudinal sides (104, 104') and two parallel, opposing transverse sides (105, 105'), the transverse sides (105, 105') being provided with grooves (301, 302, 301', 302') adapted to form an insertion channel when two panels are laid next to each other along their transverse sides (105, 105') in a common laying plane; and at least one extraneous locking element adapted to be received by said insertion channel along an insertion direction in parallel to the transverse side to lock two adjacent panels to each other relative to a first direction parallel to their common laying plane and perpendicular to the transverse sides (105, 105') as well as relative to a second direction perpendicular to their common laying plane, the extraneous locking element having a longitudinal dimension and a cross-section perpendicular to said longitudinal dimension which substantially forms a cross with at least four cross arms (901, 902, 903, 904),), wherein said grooves (301, 302, 301', 302') are oriented in such a manner that each of the cross arms (901, 902, 903, 904) is oriented diagonally between said first and said second directions when said extraneous locking element is received by said insertion channel, characterized in that a compensation groove (305, 306) extending substantially in parallel to the transverse sides (105, 105') with two substantially parallel flanks is provided between two adjacent panels when said panels are laid next to each other along their transverse sides (105, 105') in a common laying plane, such that a lower part of the compensation groove extends all the way from the insertion channel to the lower panel surface, and an upper part of the compensation groove extends from the insertion channel upwards at most partially towards the upper panel surface.