Medical image compressions allow large volume data to be kept in an exceedingly quantity of disk and to move towards complete film-less imaging. Also, the image compression process minimizes the time while download or sent the image from the internet. For that, several wavelets are used for image compression, which composed of multi-resolution based function. The choice of the suitable wavelet technique depends on the image content and there is no universal technique for all images. This paper addresses the problem of compressing the images, especially to determine whether the wavelet technique can obtain stable and accurate results for medical image compression. We analyze most wavelet techniques like: Haar, Daubechie, Biorthogonal, Coiflet, Symlets, 5/3 and 9/7 lifting technique for image compression. Then, the performance of these techniques are evaluated by the Peak Signal to Noise Ratio (PSNR), Transforming Time (T), Encoding time, Decoding time, Compression Time (CT) and Mean Square Error value (MSE). The studied wavelets are applied to the challenge medical images likes: magnetic resonance (MRI) for posterior cruciate ligament, computer tomography (CT) of the brain and retina; with varying size images to prove their efficiency. A direct benefit of this study is being able to determine the most suitable wavelet techniques for given application medical images.