Hi 3image - yes like Brian writes above the Transform > Deform > Flow command is what you would want to use to map a straight object onto a bendy one.

There is some information and examples on flow here: http://moi3d.com/3.0/docs/moi_command_reference8.htm#flow

The most simple way to use it is to draw in 2 "backbone" curves, the backbone for your straight piece with the ridges would be a line running down the middle of the shape. Then you'd draw a bendy curve over to the right. Then select the ridged shape, run Transform > Deform > Flow, and when the prompt says "Select base curve or surface", select that line running down the center as the base curve, then on the next prompt select the bendy curve as the target curve and the shape will get deformed to follow the curve.

That's probably the easiest but also curve to curve Flow will be more like transforming to a uniform tube going around those curves, it looks like you've got some variation in the shape there where your target shape is squished in one direction. It might be easiest to squish your base object in that one direction first before doing the curve to curve flow or otherwise you can do a more detailed deformation by doing surface-to-surface flow where you construct base and target surfaces to map between instead of base and target curves. You would need to get your target surface to be one single surface to use surface-to-surface Flow, right now it's constructed of separate faces. So something like extract several cross sections using Construct > Curve > Iso and then loft one large single surface through those. Also you might have problems near the swoopy end where it's bending fairly tightly, it would probably get bunched up in that area.

- Michael