A pet door system comprising: a casing (7, 207) configured to attach the pet door system to a building; and a segmented door (1, 201) attached to the casing (7, 207), wherein the segmented door (1, 201) comprises a plurality of rigid interlocking segments (2, 202) that are rotatable with respect to each other, wherein the segmented door (1, 201) is a flap configured to be pushed out of a plane of the casing (7, 207) by a pet to allow entry and exit of the pet, wherein the segmented door (1, 201) is moveable in and out of the plane of the casing (7, 207) such that the segmented door (1, 201) is capable of being pushed open, characterized in that each interlocking segment (2, 202) comprises a curved recess at a first end of the interlocking segment (2, 2. 202) defining two free legs (25,26) a opposite sides of the recess, a curved projection at an opposite second end, and two grooves (30, 31) at a portion of the curved projection farthest from the second end, wherein the two grooves (30, 31) are shaped and sized to correspond to the ends of the two free legs (25, 26), wherein the curved recess and the curved projection are shaped such that a curved projection of a first individual interlocking segment is installed within a curved recess of a second individual interlocking segment, such that the two interlocking segments are connected to each other and the curved projection of a first interlocking segment can rotate in the curved recess of a second interlocking segment, wherein the amount of rotation of the interlocking segments to one another is defined by gaps (34, 35) obtained by the free legs (25, 26) extending into the grooves (30, 31) of a neighbouring interlocking segment. a casing (7, 207) configured to attach the pet door system to a building; and a segmented door (1, 201) attached to the casing (7, 207), wherein the segmented door (1, 201) comprises a plurality of rigid interlocking segments (2, 202) that are rotatable with respect to each other, wherein the segmented door (1, 201) is a flap configured to be pushed out of a plane of the casing (7, 207) by a pet to allow entry and exit of the pet, wherein the segmented door (1, 201) is moveable in and out of the plane of the casing (7, 207) such that the segmented door (1, 201) is capable of being pushed open, characterized in that each interlocking segment (2, 202) comprises a curved recess at a first end of the interlocking segment (2, 2. 202) defining two free legs (25,26) a opposite sides of the recess, a curved projection at an opposite second end, and two grooves (30, 31) at a portion of the curved projection farthest from the second end, wherein the two grooves (30, 31) are shaped and sized to correspond to the ends of the two free legs (25, 26), wherein the curved recess and the curved projection are shaped such that a curved projection of a first individual interlocking segment is installed within a curved recess of a second individual interlocking segment, such that the two interlocking segments are connected to each other and the curved projection of a first interlocking segment can rotate in the curved recess of a second interlocking segment, wherein the amount of rotation of the interlocking segments to one another is defined by gaps (34, 35) obtained by the free legs (25, 26) extending into the grooves (30, 31) of a neighbouring interlocking segment.