A new numerical method is presented for the steady-state and transient, two-phase, lumped parameter thermal-hydraulic analysis of the fluid flow distributions in fuel pin bundles and nuclear reactor cores. The method uses the same physical model as the COBRA-IIIC code, but is based on the alternative numerical concept of generating a system of semi-implicit difference equations for the pressure field using a spatial differencing scheme that is different from the schemes previously used by subchannel analysis codes. The flow and enthalpy distributions in the lattice are found by marching downstream several times in succession between adjacent computational planes and by combining the computed pressure fields from these planes together into a composite pressure field, which is then used as the driving force for the cross-flow distribution in a reformulated form of the transverse momentum equation. The method is extremely efficient from a computational point of view and is compatible with a variety of iterative techniques, because the coefficient matrices governing the pressure field can be shown to have diagonal dominance and a simple, predictable band structure for a variety of subchannel numbering schemes. The numerical method has been integrated into the computational framework of the COBRA-IIIC code, and a new computer code has been written called COBRA-IIIP/MIT (P for a pressure solution). The code is considerably faster and more powerful than many other reactor thermal-hydraulic analysis codes and has the capability of solving extremely large and complex problems with great speed. Calculations are presented in this paper in which the results of the new code and the numerical method on which it is based are compared to those of COBRA-IIIC.