Canned dog and cat food will last for years.(The only thing is you have to be careful that you don't store dented or punctured cans which can spoil and create a horrible odor.) I buy in large quantities when it is on sale and rotate it. I think most stores will special order the quantity you need. I have an arrangement with a store to special order the flavors I want and pick them up directly from the stockroom instead of the store shelves.
Look for online coupon sites where you can get lots of coupons. That will save you quite a bit. I save about $300 dollars monthly on pet food by using coupons.
Don't forget to stock up on vitamins, medications, antibiotics, flea medication, leashes, harnesses, muzzles, carriers, bedding, towels, puppy training pads, bandages, Elizabethan collars, pet first aid books, etc.
I recommend Pet Tinic, Nutrical, Pet Tabs as supplements for pets who are sick, stressed, or not eating properly. Pet Tinic, which comes in gallon containers, 4 oz. or 8 oz. bottles, can be stored long-term. Nutrical is a paste, which can become sugary if stored long term. Pet Tabs are available in both liquid and pill form.
As with people, it is helpful if you are on good terms with your vet and able to obtain some emergency medicines for your pets.
DAP is used for calming dogs and Feliway is used for calming cats. Natural herbals can also be used. If you have to leave your pet with someone else or at a kennel, it is a good idea to leave a scented article of your clothing with your pet to comfort them. (Place an unwashed t-shirt in their cage, or, if you don't have one, use a towel or blanket which you have rubbed on your inner wrists to pick up your scent.)
If you are in a cold climate, store straw and 100% wool blankets or wool sweaters in case the power is off.
Don't forget to store extra feed and bedding for farm animals as well as insulate the buildings they live in.
Have an emergency evacuation plan for your animals as well as defense plans to protect them from thieves.