During the offshore drilling operations by drillships or semisubmersible vessels the drillstring in its first drilljoint to the Kelly suffers bending due to float vessel roll or pitch. The cyclic bending stress at any point along the drillstring, is a function of the roll or pitch angle, Kelly position in bushing, and hookload. The cumulative fatigue damage of the drillpipe due to cyclic stresses near the drillpipe connection to Kelly has been calculated in this paper. The effects of the cyclic stress amplitude variation are also taken into account. Then five multiaxial fatigue models are evaluated under variable amplitude loading (similar to drillpipe loading) conditions. Comparing the results of the five models predictions by the muliaxial fatigue tests experimental data under variable amplitude axial-torsional loading, show that the combined critical plane and energy models predict the fatigue life better than the others. It works much better for variable amplitude loading than the existing models.