[en] The pebble bed reactor's cylindrical core volume contains a random bed of small, spherical fuel-moderator elements. These graphite spheres, containing a central region of dispersed coated-particle fissile and fertile material, are cooled by high pressure helium flowing through the connected interstitial voids. A mathematical model and numerical solution technique have been developed which allow calculation of macroscopic values of thermal-hydraulic variables in an axisymmetric pebble bed nuclear reactor core. The computer program PEBBLE is based on a mathematical model which treats the bed macroscopically as a generating, conducting porous medium. The steady-state model uses a nonlinear Forchheimer-type relation between the coolant pressure gradient and mass flux, with newly derived coefficients for the linear and quadratic resistance terms. The remaining equations in the model make use of mass continuity, and thermal energy balances for the solid and fluid phases