Snakes CAN climb stairs.
If the stairs are textured giving it something to grab onto to propel it forward, snakes can climb stairs. (For example a low, wide set of brick stairs) Though they can even climb textured walls, snakes rarely enter homes in this manner. A snake needs to propel itself forward by gripping the surface upon which it is resting so the odd shape of stairs as well as the step overhang present on most stairs would likely deter most snakes from attempting to climb them. Snakes are more likely to enter the home through any outside opening that is larger than a quarter such as cracks in foundation or low lying drying vents.
Can Snakes Climb?
Though stairs are not the first objects that come to mind when considering a snake's climbing abilities, many snakes climb trees in search of prey. They are able to climb vertically by gripping the bark of the trunk and branches to propel them forward. A recent study conducted at the University of Cincinnati demonstrated that snakes, even large snakes such as the boa constrictor, can climb rope hanging vertically.
How Do Snakes Move?
In order to understand how snakes can climb, it is important to understand how it uses its unique anatomy for location. Snakes primarily employ four gaits of movement lateral undulation, concertina, rectilinear, and sidewinding.
Lateral undulation, also called serpentine locomotion, is the motion that likely comes to mind when you think of the word slithering. With this movement the snake uses it dorsal muscles to bend portions of its body in waves to push itself off of an object in order to propel forward. It will continue to propel forward following the path of the head and neck.
Concertina locomotion involves the snake bunching itself up then propelling itself forward. Snakes use this movement when they are in tight places such as tunnels.
Rectilinear location, as the name implies, is movement in a straight line. In order for the snake to accomplish this, it uses the scales on its underside to grip the ground in multiple spots and pull itself forward.
Sidewinding moves the snake's body in a diagonal pattern. The movement itself is similar to lateral undulation except the snake lifts portions of its body off the ground. Rather than the head remaining in one path, the snake throws it forward while the remainder of the body follows, which accounts for the diagonal path.