Abnormal decay patterns in attenuation are investigated for longitudinal ultrasonic waves in cylindrical rods. These abnormal patterns seem to be caused by two effects. (1) One is the interference between several modes excited in the rod by a quartz crystal transducer: McSkimin's analysis can well explain the observed results. (2) The other effect is caused by residual stresses or the fiber structure which are believed to be produced in the process of forming the material: the appropriate annealing is effective for eliminating this effect for some material. A formula is derived to discriminate whether the abnormal decay is due to the interference between the first mode and the second mode or not.