No offense to anyone that works in HR, but the impression I am getting is that HR personnel is, generally speaking, just a robot that really has no clue what they are even looking for when they see an app or resume. I have applied for several jobs that I am more than qualified for, and just for chits & grins, applied for jobs that I am WAY over qualified for. Haven't received so much as an e-mail response. What the heck are these people looking for?? How do you get to talk to somebody when your experience is technical in nature, and the HR person doest have a clue? Whats the trick to getting around the wall and getting your resume into the hands of a manager that knows what they are looking at?
Might I suggest that since you have had this issue with multiple companies, the problem might be in how you are presenting yourself as a candidate?
My wife IS this HR person. Her job is to find the absolute best candidate for that position. Her job is NOT to find you a job!
She doesn't know you. You may be the best qualified and most charming person in the world, but all she knows about you is that resume, and since she has to go through a few thousand every week your resume will get the same 30 seconds of her time as every one else's.
Do you know how to go through a thousand resumes?
"Nope Nope Nope Nope Nope
Yup
Nope Nope Nope Nope Nope Nope..."
If you try to go around HR you will fail, because that indicates you cannot follow procedure and process and she will toss you.
Not knowing you at all, I would guess that since you are getting no reaction from multiple companies you have a resume problem. Invest some time and possibly some money in researching how to improve your resume.
Is it clear?
Is it error free?
Does it make grammatical sense?
Does it adequately represent your goals and experience and objectives?
IS IT SCANNABLE?
And most importantly, did you write this one resume for this one job, incorporating the key words from the posting in the resume? If you are sending the same resume to different jobs you will not get a response.
Finally, you asked "what the heck are these people looking for?" Well, they want what is in the job posting, word for word. Example-
Midwest paint manufacturer looking for aggressive self starter to manage yellow paint operation
Your resume must not say 20 years experience manufacturing paint. It must say "I am an aggressive self starter with over 20 years experience manufacturing yellow paint" And if the next company is looking for someone to manufacture blue paint, rewrite the resume.
Send their words back to them!
Good luck!