One of the things a massage therapist should tell you prior to getting a massage is that you only need to get undressed as far as you feel comfortable. This would be for such modalities as Swedish massage or any techniques that use oils, creams or lotions and where the massage therapist would be using long, gliding strokes or kneading strokes. For most people this means leaving on only your underpants. For those who require more modesty, it may be more advantageous to request acupressure or other modalities that are effective with clothing on and use no lubricants.
Massage therapists are required by law to use adequate draping on clients. This means that a large towel or sheet should be arranged to cover all body parts that are not being worked on. Breast and groin areas should be covered at all times. So even if you are undressed, your body is covered and modesty is maintained.