In stress analysis of cracked plates, alongside the stress intensity factor which quantifies the singular stress component perpendicular to the crack plane, the role played in crack growth by the constant term parallel to the crack plane, called the T-stress, has been widely investigated by many researchers. There are, however, cases of practical interest where the influence on the stress field of the higher order terms in the series expansion for the crack tip stress field, is not negligible. The main aim of the present investigation is to present and apply a set of equations able to describe more accurately the stress components for those cases where the mode I and mode II stress intensity factors used in combination with the T-stress are unable to characterise with sufficient precision the complete stress field ahead the crack tip. The starting point is represented by the Williams’ solution (Williams, 1957) where stresses as expressed in terms of a power series. An example is investigated of a thin-thickness welded lap joint characterized by various joint width to thickness ratios, in the range of d/t ranging from 0.5 to 5. The present paper indicates that the local stresses as well as the strain energy averaged over a control volume which embraces the slip tip, can be evaluated with satisfactory precision only by taking into account a further four terms besides KI, KII and T-stress.