A computer system that employs a solid-state memory device as a physical storage resource includes a hypervisor that is capable of supporting TRIM commands issued by virtual machines running in the computer system. When a virtual machine issues a TRIM command to its corresponding virtual storage device to invalidate data stored therein, the TRIM command is received at an interface layer in the hypervisor that translates the TRIM command to a SCSI command known as UMMAP. A SCSI virtualization layer converts the UNMAP command to a file system command to delete portions of the virtual storage device that is maintained as a file in the hypervisor's file system. Upon receiving the delete commands, the hypervisor's file system driver generates a TRIM command to invalidate the data stored in the solid-state memory device at locations corresponding to the portions of the file that are to be deleted.