That used to be the problem on my 95. Untill I got new tires and a good alignment and balance. Thats exactly what mine did and I had to have my front axel replaced
Bad enine mounts
I have the same problem on my Mitsubishi Eclipse RS 1995. Seems to be a problem in Map sensor. I was also told it might be the ECU
If your 1999 4 cyl Mitsubishi Eclipse shakes when you reach 70 mph, you may need to replace your tires. Edit: I recently replaced my four tires so I don't think it would be the tires though.
bad engine mounts
Thankfully mine does not shake, thanks for asking. This is really not enough information to diagnose the problem. Does it shake the same every time or does it not shake or shake less sometimes? Is the "check engine" light on? Is there a speed where the shake is more pronounced? Does it have to be full throttle acceleration or does it shake under light acceleration too? Is there a noise accompanying the shake? If you accelerate around a corner is the shake any different? Left or right turn make a difference?
Belts broke in tires
Your tires are unbalanced. You need to get them balanced.
could be a broken engine mount
Most likely broken motor mounts.
My guess would be wheel balance.
'Agitate', maybe?
Check tire balance or wheel bearings in front axle