Here we have an amazing shot of a carpet snake eating a monster-sized chicken. Carpet snakes are approximately 2 meters long. Hanging upside down, the snake will swallow the whole thing. Note how it eats its prey headfirst, as do all constrictors.
Once, it was thought that death by constriction was caused by asphyxia or suffocation, with the snake holding its prey too tightly to allow the prey to take a breath, but new research shows the death comes through different means (and what the snakes don't do is crush their prey to death, as myth would have it).