The self-discovery of a suspicious symptom often brings about an emotional turbulence: while recognizing the importance of having the symptom diagnosed promptly, individuals frequently delay diagnosis, seeking to avoid the pain or discomfort associated with the diagnostic process and fearing to hear that they are developing a serious illness. The present paper proposes a rational, economic-oriented approach to explaining individuals' delay behavior, weighing the fear of the diagnostic procedure and of being told the suspected truth against the fear of consequence of further procrastination. Assuming that the money costs of diagnosis and medical treatment are borne by health insurance, a multi-period expected-utility maximization model is constructed to inquire into the individual's decision of whether and to what extent to delay diagnosis. The results rationalize a variety of observed behavior concerning individuals' reaction to suspicious symptoms that differ in their psychic cost of diagnosis, the likelihood of indicating severe illness and the potential damage to health incurred by delayed diagnosis. The desirability of delayed diagnosis to the health insurer and the socially desired solution are finally discussed.