Many owners are reluctant to bring their cats to the veterinarian because of the difficulty of getting their cat into the carrier and the fact that many cats are extremely stressed by riding in a car. The waiting room itself induces anxiety simply due to the fact that it is a strange place. Of course the sound and scent of dogs is extremely frightening for most cats. At Mahomet Animal Hospital we have a separate waiting room for cats that will help reduce this fear. We also have tables to rest the carriers on as cats feel more secure in an elevated position.
The following is an article by Dr. Sophia Yin on how to get your cat used to the carrier:
LOW STRESS HANDLING, RESTRAINT AND BEHAVIOR MODIFICATION OF DOGS & CATS
Dr. Sophia Yin, DVM, MS www.drsophiayin.com
Training Cats to Love Their Carriers
Overview of Behavior Modification Terms and Processes
OVERVIEW
To those who are new to the concept of crate training, confinement in such a small space might seem like some sort of medieval torture. But free-roaming dogs seek shelter in small, enclosed spaces and feral cats hide in small, dark spaces to avoid being eaten by coyotes and other predators. In fact, anyone who’s visited a person with cats knows that when unfamiliar people enter their home, many cats immediately run for cover in places much smaller than a comfy travel carrier. Based on this natural history, one can see how pet dogs and cats can easily be trained to perceive a travel carrier or crate as a cozy cave or a home away from home (and one that can be taken with them wherever they go). In fact, all dogs and cats should be trained to enjoy being in a travel carrier or crate so they feel comfortable traveling. For dogs, in particular, learning to enjoy staying in their crates for extended periods of time can be important for teaching them that it’s okay to be alone in their “bedroom.” Then they’ll be less likely to develop anxiety when separated from their owners down the road.
Training pets to see their crate or carrier as their personal bedroom is simple even for cranky cats, and usually takes less than a week. It’s all about teaching them that great things happen when they’re in their crate. The great thing we will use is food. Throughout the process, other motivators can be used, as well.

If the cat really dislikes being confined, start by feeding her daily meals just outside the carrier.

When she’s comfortably eating her meals in this new location, move the food just inside the carrier so she has to stick her head in to eat.

She should readily stick her head in. When she’s comfortable, she’ll eat the meal without backing out to look around.

In this manner, gradually move the food dish farther in until the cat easily goes all the way into the carrier.

For most cats, getting to this point takes less than 3-4 days.

Hide tasty treats or toys (whichever she’s most motivated by) in the carrier for her to find throughout the day. The goal is for her to learn to explore the carrier for treats or toys.

The cat should always readily enter the carrier and walk out in a relaxed manner. If she looks vigilant or rushes out, then work in more gradual steps.

How do you know when the cat loves her carrier? When she randomly enters and lies down to rest on her own. Some cats even choose to sleep in their carriers.

Once the cat comfortably enters her carrier to rest, the carrier door can be closed during her meal, and she can be kept in the carrier for short periods of time. Gradually work up to enclosing her for longer sessions. This step is optional for cats, whereas for dogs it’s required. Cats often adapt better than dogs to being in travel carriers.
Completing these simple steps will train your house cat to think that his carrier is a heavenly haven.