The elastic cap includes a cap body, a cap bill joined to the cap body, a sweatband secured to a lower periphery of the cap body, and a strip of core wrapped by the sweatband. The sweatband is constructed with a stretchable material. The strip of core is constructed with a non-stretchable material having a liquid absorbent or liquid draining property. The strip of core extends over a forward portion of the sweatband adjacent to the cap bill, but does not extend in a rear portion of the sweatband which is remote from the cap bill.