The Mars Pathfinder probe will enter the Martian atmosphere at a relative velocity of 7.65 km/s. The 2.65-m-diam vehicle has a blunted, 70-deg-half-angle, conical forebody aerobrake. Axisymmetric time-dependent calculations have been made using Gauss-Seidel implicit aerothermodynamic Navier-Stokes code with thermochemical surface conditions and a program to calculate the charring-material thermal response and ablation for heating analysis and heat-shield material sizing. The two codes are loosely coupled. The flowfield and convective heat-transfer coefficients are computed using the flowfield code with species balance conditions for an ablating surface. The time-dependent in-depth conduction with surface blowing is simulated using the material response code with complete surface energy-balance conditions. This is the first study demonstrating that the computational fluid-dynamics code interfacing with the material response code can be directly applied to the design of thermal protection systems of spacecraft. The heat-shield material is SLA-561V. The solutions, including the flowfield, surface heat fluxes and temperature distributions, pyrolysis-gas blowing rates, in-depth temperature history, and minimum heat-shield thicknesses over the aeroshell forebody, are presented and discussed in detail. The predicted heat-shield mass is about 20 kg.