Is this a case for Mixed Model Anova?

My study has 2 IV's each with two levels (2 hull designs and 2 techniques) = 4 conditions, and has 3 subjects. Max acceleration data was gathered for each subject over 5 trials on the same day.Hence I have 5 x 4 values for each subject.
I would like to perform ANOVA on the results without averaging each subject's data first (which I believe may reduce the power of the information I have collected). The best situation would be for me to be able to average the results I agree, but due to H & S limitations in the experiment the 3 subjects is all I have.
I have read somewhere that I may be able to treat the subject as a random variable?
Any advice on a suitable test would be greatly appreciated!!
Many thanks