An elevator comprising a hoistway; an elevator car vertically movable in the hoistway; at least one rope (3a,3b,3c) connected to the car; a rotatable traction member comprising a circumferential traction surface (4a, 4b, 4c) for each of the at least one rope (3a,3b,3c); each of the at least one rope (3a,3b,3c) passing around the rotatable traction member and having a front side surface (5a,5b,5c) resting against a circumferential traction surface (4a, 4b, 4c) of the traction member; and a drive machinery for controlling rotation of the rotatable traction member; and activatable pressing means for pressing the at least one rope (3a,3b,3c) against the circumferential traction surface (4a, 4b, 4c) of the traction member which comprise a pressing shoe mounted on the back side of and out of contact with the rope section (13a, 13b, 13c) of each of said at least one rope (3a,3b,3c), which rope section (13a,13b,13c) rests against the rotatable traction member, the pressing shoe being movable towards the back side surface (9a, 9b, 9c) of said rope section (13a, 13b, 13c); and actuating means (14,15) activatable to move the pressing shoe towards the back side surface (9a, 9b, 9c) of said rope section (13a, 13b, 13c) such that the pressing shoe moves into contact with and presses the rope section (13a,13b,13c) against the circumferential traction surface (4a, 4b, 4c) of the traction member; and activating means (10,10',10",20,100) for activating the actuating means (14,15) to move the pressing shoe towards the back side surface (9a, 9b, 9c) of said rope section (13a, 13b, 13c); characterized in that the front side surface (5a,5b,5c) of each of the at least one rope (3a,3b,3c) and/or the traction surface (4a, 4b, 4c) of the rotatable traction member is made of material comprising polymer, and the elevator comprises one or more sensing means (10,10',10") comprising a temperature sensing means, and an increased temperature sensed by the sensing means is arranged to cause the drive machinery to stop the rotation of the rotatable traction member, and activation of the actuating means (14,15). a hoistway; an elevator car vertically movable in the hoistway; at least one rope (3a,3b,3c) connected to the car; a rotatable traction member comprising a circumferential traction surface (4a, 4b, 4c) for each of the at least one rope (3a,3b,3c); each of the at least one rope (3a,3b,3c) passing around the rotatable traction member and having a front side surface (5a,5b,5c) resting against a circumferential traction surface (4a, 4b, 4c) of the traction member; and a drive machinery for controlling rotation of the rotatable traction member; and activatable pressing means for pressing the at least one rope (3a,3b,3c) against the circumferential traction surface (4a, 4b, 4c) of the traction member which comprise a pressing shoe mounted on the back side of and out of contact with the rope section (13a, 13b, 13c) of each of said at least one rope (3a,3b,3c), which rope section (13a,13b,13c) rests against the rotatable traction member, the pressing shoe being movable towards the back side surface (9a, 9b, 9c) of said rope section (13a, 13b, 13c); and actuating means (14,15) activatable to move the pressing shoe towards the back side surface (9a, 9b, 9c) of said rope section (13a, 13b, 13c) such that the pressing shoe moves into contact with and presses the rope section (13a,13b,13c) against the circumferential traction surface (4a, 4b, 4c) of the traction member; and activating means (10,10',10",20,100) for activating the actuating means (14,15) to move the pressing shoe towards the back side surface (9a, 9b, 9c) of said rope section (13a, 13b, 13c); characterized in that the front side surface (5a,5b,5c) of each of the at least one rope (3a,3b,3c) and/or the traction surface (4a, 4b, 4c) of the rotatable traction member is made of material comprising polymer, and the elevator comprises one or more sensing means (10,10',10") comprising a temperature sensing means, and an increased temperature sensed by the sensing means is arranged to cause the drive machinery to stop the rotation of the rotatable traction member, and activation of the actuating means (14,15).