The design of apodization and windowing functions forms the predominant part of the beamforming process in ultrasound imaging. However, the detailed analysis of apodization in the case of beamforming for flow imaging is very limited in the literature. This paper introduces the concept of dual apodization technique in vector triangulation for ultrasound-based vector flow imaging. The approach utilizes the idea of multiple apodization to induce a steering effect at receive along with sidelobe suppression for the delay compensated radio-frequency (RF) signals. The method is investigated using extensive simulations for transverse flows with different flow profiles at different velocities, which shows an improvement in resolution and better clutter suppression. The proposed approach is further analyzed using various conventional and data adaptive apodization techniques for a gradient flow profile. The error variance in velocity magnitude estimate is as low as 5.0251\times 10^{-4}\ [m/s]^{2} and the mean angle error is +0.7358° using Hanning-Gaussian apodization for a transverse gradient flow with a peak velocity of 0.25 m/s. © 2020 IEEE.