© 2002-2011 IEEE. The Large Hadron Collider Luminosity upgrade (HiLumi) program requires new low-β triplet quadrupole magnets, called MQXF, in the interaction region to increase the LHC peak and integrated luminosity. The MQXF magnets, designed and fabricated in collaboration between CERN and the U.S. LARP, will all have the same cross section. The MQXF long model, referred as MQXFA, is a quadrupole using the Nb3Sn superconducting technology with 150 mm aperture and a 4.2 m magnetic length and is the first long prototype of the final MQXF design. The MQXFA magnet is based on the previous LARP HQ and MQXFS designs. In this paper, we present the baseline design of the MQXFA structure with detailed three-dimensional (3-D) numerical analysis. A detailed tolerance analysis of the baseline case has been performed by using a 3-D finite element model, which allows fast computation of structures modeled with actual tolerances. Tolerance sensitivity of each component is discussed to verify the actual tolerances to be achieved by vendors. Tolerance stack-up analysis is presented in the end of this paper.