Many sources say you shouldn't can on a glass-top (flat-top) stove. Are they right? Yes and no. You'll have to do some research before you can make that decision for yourself.
The two main reasons that canning is not recommended on a flat-top stove are:
1. The stove can be damaged.
2. The temperature cannot be kept consistently high enough.
Let's take a look at those two reasons.
1. The stove can be damaged
a. Most flat-top stoves have a weight limit. Mine is 50 pounds. My canner holds 21 quarts; a gallon of water weighs 8.33 pounds; my canner will hold 43.7 pounds of water. Amazon says my canner weighs 7.6 pounds. That puts me at 51.3 pounds, but if I subtract two quarts of water, I'm at 47.1 pounds. (Note: I just found out that boiling water weighs significantly less: only 8 pounds per gallon, but I'm too lazy to redo the math.) (Second note: I am aware that the canner will hold jars, fruit, and sugar syrup in addition to water. But the water weight is a good enough estimate for me.)
You'll want to figure out whether this will work for you before you attempt to can on a flat-top stove. You will need the weight limit for your stove, the weight of your canner, and the capacity of your canner. But don't choose a canner until you read section 2!
b. A second reason that the stove can be damaged is that the stovetop can overheat, causing the thermostat in the burner to stop working properly or causing the stovetop to crack. We don't want that! Using a flat-bottomed canner or stockpot can minimize this risk, as can matching the burner size to the size of your canner as closely as possible.
The owner's manual for my stove recommends that pots overhang the burner by no more than 1/2". My canner goes over by about an inch. This is a risk I chose to take.
2. The temperature cannot be kept consistently high enough
a. The first reason it can be hard to keep the temperature up is that most glass-top stoves have burners that cycle on and off, even on the highest setting, to protect the stove from becoming too hot and cracking. The bottom line for me is this: if my stove can keep my canner boiling steadily for the entire processing time, I will not worry. I can keep a fairly large stockpot boiling for hours once it gets up to temperature, so I was not too worried about this. Also, my canner has a glass lid that makes it easy to monitor the water.
b. The second reason it can be hard to keep the temperature up is that most canners do not have a flat bottom. Glass-top stoves work best with flat cookware. A non-flat bottomed pot doesn't transfer heat as well, making it harder to keep the water boiling. Additionally, it could possibly cause excessive cycling of the burner, making it even harder to keep a steady boil. The lesson here is: get a flat-bottomed canner.
To minimize risk of excessive weight and too low temperature, you could can in a smaller flat-bottomed pot with a rack at the bottom. You can can in any pot in which you can maintain a steady boil with water at least 1 inch over the tops of the jars. You can also buy special short canners that work for pint jars and smaller.
You could also use a camping stove outside. This is outlined thoroughly in the first link listed below.
These are my own thoughts, gained mostly from non-scientific articles and reviews. Your personal equipment and opinions may differ, so please do your own research before deciding whether canning on your glass-top stove is a good idea. Proceed at your own risk!
You should take my decision to can on my flat-top stove with a grain of salt: I regularly disregard laundering instructions on clothing tags; I don't use HE detergent in my HE washing machine; I have nearly killed my KitchenAid mixer; and I have burned out three blenders. That's just the kind of person I am. Reckless! You probably shouldn't listen to me.
P.S. I did choose to can on my flat-top stove, and everything went beautifully and the stove did not crack.
Material I read for research (most helpful are starred)
The owner's manual for my stove (and I spoke with customer service because it wasn't very specific)*
The Amazon reviews and product description on the canner I bought