Multi-beam tunable diode laser absorption spectroscopy (TDLAS) can be used to estimate the mass flow rate in a complex, inhomogeneous flowfield. The cost and complexity of a TDLAS array increases with the number of beams, but additional beams do not necessarily improve the accuracy of estimates. To-date, the arrangement of beams in TDLAS mass capture sensors has been heuristic, and there is a need for a mathematically-rigorous design strategy and trade study. We present a technique to optimize the location and orientation of multiple TDLAS beams for mass flow sensing. Our optimization technique is based on a statistical objective function that minimizes the uncertainty of estimates, subject to spatial uncertainties and measurement noise. The objective function can be augmented with prior information derived from computational models and previous measurement campaigns. Our function is based on a novel, linear formulation of absorption tomography with velocimetry, which enables the tractable computation of an expected posterior probability density function. Minimizing the posterior uncertainty maximizes one’s confidence in estimates of mass capture. Our metric provides general guidance for the arrangement of a multi-beam TDLAS mass flow sensor, and does not depend on the use of tomographic reconstruction.