A water craft allows a user to travel across a surface of water utilizing a natural walking motion, which employs arms and legs for propulsion similar to cross-country snow skiing. The water craft includes a pair of skis adapted to fit on the user's feet. The skis can be coupled together by semi-elastic tethers. Each ski can include a foot well for receiving the user's foot. The foot well is designed to simulate the natural walking motion of the user. The user can propel the water craft using tail paddles and ski poles. The tail paddles are coupled to the rear of the skis. The tail paddles are configured to float on the water and to rotate about a transverse axis of the skis. The tail paddles are shaped to grip or "dig in" the water in response to the user moving the skis in a direction opposite the direction of motion of the water craft. The tail paddles provide resistance to propel the water craft when the ski is moved backward and slide along the water when the skis move forward. The ski poles include a paddle shaped to grip or "dig in" in response to the user pushing backwards on the ski poles. The paddle provides resistance to the backwards motion to propel the water craft forward. When the user pulls the ski poles forward, the paddles surface and slide across the water as the water craft moves forward.