1. An apparatus for measuring subcutaneous fat thickness by ultrasound, comprising: a central processing unit (CPU) and associated memory; a transducer for sending ultrasound pulses and receiving ultrasound echoes; computer program code stored in the memory and executed by the CPU; the apparatus controlled by the CPU performs functions comprising: applying a first amount of pressure to the transducer in contact with a skin spot; sending a first one or more ultrasound pulses from the transducer while applying said first amount pressure on said skin spot; receiving a first set of echoes; deriving a first plurality of echo peak positions from the first set of echoes; applying a second amount of pressure to the transducer in contact with said skin spot, wherein said second amount of pressure is different from said first amount of pressure; sending a second one or more ultrasound pulses from the transducer while applying said second amount pressure on said skin spot; receiving a second set of echoes; deriving a second plurality of echo peak positions from the second set of echoes; distinguishing echoes generated at a fat-muscle boundary from echoes generated at muscle-bone boundaries based on time delay changes between said first plurality of echo peak positions and said second plurality of echo peak positions; determining at least one echo as being generated at the fat-muscle boundary if said at least one echo has a time delay change being smaller than a first threshold; calculating the subcutaneous fat thickness based on the determined at least one echo as being generated at the fat-muscle boundary.