It is generally accepted that human cancers grow in an exponential or Gompertzian manner. This assumption is based on analysis of the growth of transplantable animal tumors and on averages of tumor growth in human populations. A computer model of breast cancer in individual patients has raised some doubts about this assumption. The computer model predicts an irregular pattern of tumor growth that incorporates plateaus or dormant periods separated by Gompertzian growth spurts. Since growth patterns involving plateaus are not predicted by conventionally accepted exponential or Gompertzian kinetics, sufficient documentation of their existence may be regarded as some evidence that the computer model is correct. The literature has been surveyed to identify growth patterns specifically predicted by the model. The literature contains clinical evidence from individual patients of this growth pattern in primary breast, large intestine and rectum, and pulmonary cancers and metastatic pulmonary cancer. Much data, including the only breast data, are not consistent with exponential or Gompertzian kinetics but are explainable by irregular growth kinetics. Exponential growth is valid for some tumors and for short times, but there are many papers citing significant deviations from that growth. Exponential growth may accurately describe averages of human tumor growth and growth of multipassaged experimental tumors, but it is not valid for all individual tumors.