Why does your 1992 Crown Vic V8 shudder at around 30 to 40 MPH?

Check the front end bushings, make sure they are not worn out. Check for bent suspension components. Check for out of balance tires. If happens when accelerating only, and when going over 33mph only (like coming out of a school zone) then it's your torque converter that's going out. You need a new one but probably don't want to invest another $600+ in that older car. Add a small bottle of GM "Limited Slip Additive" to your tranny. Might buy you another year with it.