The purpose of this paper is to propose blood flow measurement algorithms under non-periodic displacement of an artery by controlling an ultrasound (US) probe. Detecting the position and velocity of a bleeding source is required as the first step in treating internal bleeding in emergency medicine. However, the current methods for detecting a bleeding source involve an invasive approach and cannot quantitatively estimate the velocity of bleeding. Therefore, current emergency medical care requires an alternative system to address these problems. In this study, we aim to develop a blood flow measurement system for detecting a bleeding source by using a non-invasive modality, such as a US imaging device. Some problems related to the measurement error still need to be addressed before we can create this system. In particular, the blood flow measurement error in the abdominal area is typically large because the displacement of the artery is too large and non-periodic to adequately control the probe. As the first step in solving these problems, we focused on the displacement of the artery towards the out-of-plane state of a US image and developed measurement algorithms to control the probe under the displacement based on respiratory information. We conducted cross-sectional area and flow rate measurement experiments using an ultrasound phantom containing an artery model and a manipulator equipped with a US probe (BASIS-1). The results represent the first experimental validation of the proposed algorithms.