In breast cancer screening, the automated breast volume scanner (ABVS) was introduced as an alternative for mammography since the latter technique is less suitable for women with dense breasts. Although clinical studies show promising results, clinicians report two disadvantages: long acquisition times (>90?s) introducing breathing artefacts, and high recall rates due to detection of many small lesions of uncertain malignant potential. Technical improvements for faster image acquisition and better discrimination between benign and malignant lesions are thus required. Therefore, the aim of this study was to investigate if 3D ultrasound elastography using plane-wave imaging is feasible. Strain images of a breast elastography phantom were acquired by an ABVS-mimicking device that allowed axial and elevational movement of the attached transducer. Pre- and post-deformation volumes were acquired with different constant speeds (between 1.25 and 40.0?mm s(-1)) and by three protocols: Go-Go (pre- and post-volumes with identical start and end positions), Go-Return (similar to Go-Go with opposite scanning directions) and Control (pre- and post-volumes acquired per position, this protocol can be seen as reference). Afterwards, 2D and 3D cross-correlation and strain algorithms were applied to the acquired volumes and the results were compared. The Go-Go protocol was shown to be superior with better strain image quality (CNRe and SNRe) than Go-Return and to be similar as Control. This can be attributed to applying opposite mechanical forces to the phantom during the Go-Return protocol, leading to out-of-plane motion. This motion was partly compensated by using 3D cross-correlation. However, the quality was still inferior to Go-Go. Since these results were obtained in a phantom study with controlled deformations, the effect of possible uncontrolled in vivo tissue motion artefacts has to be addressed in future studies. In conclusion, it seems feasible to implement 3D ultrasound quasi-static elastography on an ABVS-like system and to reduce scan times within one breath-hold (~10?s) by plane-wave acquisitions.