It has long been non-destructively evaluated on weld joints of various pipes which are indispensable to most of industrial structures. Ultrasound evaluation has been used to detect flaws in welding joints, but some technical deficiencies still remain. Especially, ultrasound imaging on weld of elbow pipes has many challenging issues due to varying surface along circumferential direction. Conventional ultrasound imaging has particularly focused on ultrasonic wave propagation based on ray theory. This confines the incident angle and the position of an array transducer as well. Total focusing method (TFM), however, can provide not only high resolution images but also flexibility that enables to use ultrasonic waves to every direction that they can reach. This leads us to develop a method to get images of weld zone from an elbow part that curves. It is inevitable of each ultrasonic wave from the array transducer to transmit through different media and to be reflected from the boundary with angles along the curved surface. To form a correct PA image, careful calculation is made to ensure that time delay of receive-after-transmit is correctly shifted and summed even under non-planar boundary condition. Here, a method to calculate wave paths for the zone of interest at weld joint of an elbow pipe is presented. Numerical simulations of wave propagation on an elbow pipe are made to verify the proposed method. It is also experimentally demonstrated that the proposed method is well applied to various actual pipes that contains artificial flaws with a flexible wedge.