An infinite plate to which a narrow infinitely long beam is attached rigidly and continuously may be considered as an idealization of some typical flight vehicle structures. Reflection, transmission, and near‐field effects, associated with a straight‐crested flexural wave impinging on one side of the beam, are presented as functions of the properties of the plate and beam and interpreted in terms of trace matching of the flexural waves in the plate with flexural and torsional waves in the beam. The concepts of dynamic stress and strain concentration factors are discussed, and upper bounds on these factors are given. Some implications pertaining to the design of beam reinforced panel structures with favorable fatigue properties are pointed out.