"World War Z" (the book, not the movie) by Max Brooks actually covers this fairly well.
At least in my opinion, the zombies in WWZ are either some form of alien parasite, a nanite plague, or some equivalent mechanism that facilitates some rather severe changes in the zombies' biology. The internals have largely converted to a black, tar-like substance which appears to actually be providing the locomotive force. Gun shots, stab wounds, blunt beatings, etc. just pretty much don't do anything. They're spongy, soft, and simply absorb most impacts. There are no internal organs of any importance. The skeletal structure may or may not still be there, but any injury to it simply changes their mobility slightly. Their 100% immune to any bacterial, viral, or fungal infection, as whatever they've been transmuted into isn't compatible with local microbiology, so they don't rot or decay in any way, nor are do they appear susceptible to exposure. A zombie stuck in extended sub-freezing temperatures simply freezes solid and then thaws and returns to shambling around if and when temperatures increase. Trying to burn them is just as ineffective, as their new physiology has them slowly burn off their clothing and maybe an exterior layer of semi-normal-looking skin before the interior tar-substance makes the flames go out. To paraphrase the book, napalm is useless, as all you end up with is converting a bunch of slowly advancing zombies into a bunch of slowly advancing flaming zombies. And something else that the book goes into detail concerning is the complete and utter lack of fear. There is no such thing as using "shock and awe" tactics on something that literally doesn't care if it dies (since it's already dead anyway). The "Battle of Yonkers" shows this quite clearly, with the military using traditional tactics including large-scale artillery while the horde just continues advancing. A bomb might blow off a zombie's legs and throw it 20 feet to the side, but then the top half just starts clawing towards you again. Then you have the scale issues, as the numbers of infected eventually get so bad that those stuck up on the ISS can see them from space on the Midwest plains ebbing and flowing like herds of buffalo before Western colonization. And finally, you have the "call for help". The book describes the zombies calling to each other whenever "food" is located. And what's worse is that that sets off a chain reaction. Any zombie that hears a call-out will then call out again, so you have an ever-growing network effect where even just one zombie spotting you may be catastrophic. This lead to any roadway being a certain death trap. People would starve to death or dehydrate while trapped in their cars surrounded by zombies. The zombies never got to them, but then the person who died inside might become a zombie from latent infection. That car-trapped zombie then just became a standing warning signal. If somebody passed what appeared to be a deserted car on the road, and the trapped zombie noticed them, then it would call out, and any zombie in ear shot knew that dinner was served.
Tying this back to the original military-force problem, basically any military engagement would, therefore, draw enough attention that you were guaranteed a mass wave of them in a relatively short time frame. Combined with their nigh-invulnerability where literally *nothing* but a head shot was effective, and the military would simply run out of ammunition before they'd come close to dealing with the immediate threat.
Now I'm in no way saying that most zombie descriptions even come close to some of these details. And it's my understanding that Max Brooks' goal was to specifically modify the zombie milieu to account for any unbelievable aspect such as your assertion of military force being effective. So, yeah, in most cases you're right that artillery would probably work just fine. But if you're looking for somebody to try and actually make a *working* description of how a zombie plague might actually beat us, then try out the book. Avoid the movie, IMHO. It completely glosses over 90% of what I described above, which made it a standard, unbelievable scenario, unfortunately.