An egg case or egg capsule, often colloquially called a mermaid's purse, is the casing that surrounds the eggs of oviparous chondrichthyans. Living chondricthyans that produce egg cases include some sharks, skates and chimaeras. Egg cases typically contain one embryo, except for big skate and mottled skate egg cases, which contain up to 7 embryos. Oviparity is completely absent in the superorder Squalomorphi. Egg cases are also thought to have been produced by some extinct chondrichthyan groups, such as hybodonts and xenacanths.

Egg cases are made of collagen protein strands, and are often described as feeling rough and leathery. Some egg cases have a fibrous material covering the outside of the egg case, thought to aid in attachment to substrate. Egg cases without a fibrous outer layer can be striated, bumpy, or smooth and glossy. With the exception of bullhead shark eggs, egg cases are typically rectangular in shape with projections, called horns, at each corner. Depending on the species, egg cases may have one or more tendrils.

Shortly after internal fertilization, the fertilized ovum enters the partially formed egg case located in the oviduct. After the ovum enters, the rest of the egg case forms around it. Shortly after the egg case finishes developing, it is deposited outside the body; common locations include kelp forests and rocky seafloors. Egg cases are typically produced in pairs, each with one fertilized embryo inside, with the exception of a few species that produce egg cases with more than one viable embryo.

Gestation can take anywhere from a few months to over a year. After a period of development, typically a week or two, small slits open on each side of the egg case to aid water flow. The embryo fans its tail constantly to promote exchange with surrounding water.

Oviparity in sharks can be categorized as single or retained. With single oviparity, the egg cases are extruded soon after fertilization. With retained oviparity, eggs are kept within the oviduct for a period of time before depositing outside of the body as an unhatched egg case. It is thought that viviparity is the ancestral condition for sharks, and that it evolved through the elongation of retention time of retained oviparity.

Oviparous sharks are known to regularly produce unfertilized eggs when kept in captivity without males.

Bullhead shark egg cases are shaped like an auger, with two spiral flanges. This allows the egg cases to become wedged in the crevices of rocky sea floors, where the eggs are protected from predators; however, some bullhead sharks deposit their eggs on sponges or seaweed. Hatchlings are considered large for sharks, reaching over 14 cm in length by the time they leave the egg case. Bullhead shark eggs typically hatch after 7 to 12 months, depending on the species. The female Japanese bullhead shark has been known to deposit their eggs in one location along with other females, called a "nest". The egg case of the Mexican hornshark features a tendril and more rigid flanges, suggesting that egg case design of this species is evolving towards anchoring with tendrils and away from wedging into crevices. As a member of the order Heterodontiformes, the whitespotted bullhead sharks is thought to be oviparous, but egg cases have never been observed.

The bamboo sharks (Hemiscylliidae) and the zebra shark (Stegostomatidae) lay eggs on the bottom, while the other carpet sharks give live birth. The egg cases are oval and covered with adhesive fibers that serve to secure them to the bottom.