Introduction - fracture mechanics; problems addressed by fracture mechanics; numerical fracture mechanics; basic solid mechanics - elasticity; elastoplasticity; basic fracture mechanics - linear elastic fracture mechanics (LEFM); the J-integral; elasto-plastic fracture mechanics; fatigue crack growth; an elastoplastic boundary element formulation - boundary element methods in solid mechanics; application to crack problems, J-type integrals - some J-type integrals; numerical comparison of the various integrals; the elastoplastic dual boundary element method (EPDBEM) - the elastoplastic DBEM; numerical applications; application of the EPDBEM to crack contact problems - evaluation of J-type EPFM parameters; effect of residual stresses on fatigue crack growth; fatigue crack growth; numerical application (LEFM/WF); elastoplastic simulation of crack growth in the presence of residual stress fields - modelling of stable crack growth.