This is a video of a mosquito inserting itself into the flesh of a mouse in search of some blood. Scientists were able to watch the entire process through a microscope to see how a mosquito bites down. It's kinda freaky how flexible the needle can get.
National Geographic's Not Exactly Rocket Science shows what you would imagine to be a stiff as a needle (it has to puncture the skin after all), can actually get flexible when it searches for blood vessels. National Geographic writes:
From afar, a mosquito's snout might look like a single tube, but it's actually a complicated set of tools, encased in a sheath called the labium. You can't see the labrum at all in the videos; it buckles when the insect bites, allowing the six mouthparts within to slide into the mouse's skin.