This paper investigates sources of error for a vector velocity volume flow estimator. Quantification of the estimator's accuracy is performed theoretically and investigated in vivo. Womersley's model for pulsatile flow is used to simulate velocity profiles and calculate volume flow errors in cases of elliptical vessels and not placing the transducer at the vessel center. Simulations show, i.e., that volume flow is underestimated with 5 %, when the transducer is placed 15 % from the vessel center. Twenty patients with arteriovenous fistulas for hemodialysis are scanned in a clinical study. A BK Medical UltraView 800 ultrasound scanner with a 9 MHz linear array transducer is used to obtain Vector Flow Imaging sequences of a superficial part of the fistulas. Cross-sectional diameters of each fistula are measured on B-mode images by rotating the scan plane 90 degrees. The major axis of the fistulas was on average 8.6 % larger than the minor axis, so elliptic dimensions should be taken into account in volume flow estimation. The ultrasound beam was on average 1.5 ± 0.8 mm off-axis, corresponding to 28.5 ± 11.3 % of the major semi-axis of a fistula, and this could result in 15 % underestimated volume flow according to the simulation. Volume flow estimates were corrected for the beam being off-axis, but was not able to significantly decrease the error relative to measurements with the reference method.