Okay, the kind of laptop people discuss here regularly is normally SSD only, and basically everything on the market outside the absolutely basic models is available in such configurations. These links are just a few from the past weeks. The threads about the Macbooks are full of recommendations for alternatives as well. Being SSD-only really is a trivial criteria and without knowing more about what you want it's impossible to make any meaningful recommendation except "figure out what you want and then order one of that with an SSD", it's highly unlikely you won't be able to do that.
https://news.ycombinator.com/item?id=13214754
https://news.ycombinator.com/item?id=12985645
https://news.ycombinator.com/item?id=13286150
https://news.ycombinator.com/item?id=13219276