Select the shapes in the viewport, then right-click the shapes and select "Align Shapes to Terrain". There's several options there. You must select the terrain, and select an option for the projection to the terrain. Then hit Okay.
Chris is correct in his description, and this is the best way to get shapes to align to your terrain.
The Align Shapes to terrain function documentation however has several options which are described here.
Once you align shapes, often depending on the method you select you still might need to make changes to the terrain so that it matches your shapes. The way to do this is the Align Terrain to Shapes Function. This also has useful attributes in that will till you how much Cut and Fill was required to changed the terrain to match that of the shape at its current alignment (if it is relevant for your project).
Hope this is helpful.
Thanks, Chris and David. I did this but it doesn't seem that the shapefile drapes over the terrain. I made a file that shows a basemap of streets, green and buildings and land and now want that to follow the contours of the terrain. I know you can drape a raster but can you do this with Shapefiles or GDB's?
Can you post an image or two, so we can see further detail?
One problem you might get is that the vertices are the only things that are projecting, and this sometimes leaves the faces in conflict with the terrain. In the image below is what I mean, and what David describes using AlignTerrainToShapes to fix. We just need to see what you are seeing.
I have used ArcGIS (3D Analyst) to do just that. I used the tool: Interpolate PolygonTo Multipatch and then import the result to CityEngine.
I will create lots and lots of polygons...
Here's a rule for dividing shapes into grids of rectangles (attached). After running the rule on a shape and setting the grid X and Z dimensions, then select the model and convert it into shapes. Then you can run rules on the resulting multipatch, or you can do "separate faces" and run rules on the individual faces.