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I have made a ring in blender 2.71.

I have applied a subsurface smoothing modifier, and set the shading to smooth.

For some reason I don't understand, the model is covered in wrinkles.

enter image description here

When I go into edit mode, The subdivision surface appears to have a lot of curves.

enter image description here

This is causing problems when I try and apply a shrink wrap.

enter image description here I have attached the actual blender file here:

https://dl.dropboxusercontent.com/u/460997/Blender/PaveTest.blend

How can I make the surface smoother, and not have all these wrinkles?

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    $\begingroup$ The topology of your object has lots of tris, ngons, and really thin faces which are causing the subserf to look strange. Try to make your mesh a out of evenly spaced quads, and avoid ngons and tris. $\endgroup$ – gandalf3 Sep 28 '14 at 23:55
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    $\begingroup$ other ways to make a ring: blender.stackexchange.com/questions/9056/… $\endgroup$ – cegaton Sep 29 '14 at 0:40
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Your object has very irregular topology containing triangles and ngons:

enter image description here

These should be avoided as much as possible when working with the subdivision surface modifier, as they will cause strange distortions like the ones you are seeing.

When working with subsurf, try to make your object completely out of evenly spaced quads (faces with four vertices):

enter image description here

Also try to keep the normals consistently pointing outwards, otherwise you might see dark shading artifacts. You can recalculate the normals by selecting everything (A) in edit mode (↹ Tab) and pressing ⎈ CtrlN.

This will result in a much smoother surface, which makes shrink wrap give the desired result:

enter image description here

Note that the object you are shrink-wrapping is made up of tris, so subsurf isn't advisable on it either.

Example .blend

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