You might as well make a DEM/TIN (using ArcGIS) of the shapefile you have. That will give you the DEM you need to convert to GMT format.

You might as well make a DEM/TIN (using ArcGIS) of the shapefile you have. That will give you the DEM you need to convert to GMT format.

After a quick Google search, I found a couple of links..

convert SRTM30 data to grd

Shapefile to GMT DEM file

Also check the this PDF, mostly after the 15th Page - GMT and Gridded Datasets

There is a clear cut procedure for convering the DEM data to GMT data. Conversion from shapefile to DEM is fairly simple, as you have already achieved it.