Most image and video coding techniques are based on the method of Discrete Cosine Transform (DCT) after partitioning the image into square blocks. This method is called block DCT (BDCT). It is considered as one of the best methods of image and video compression. However, in cases of high compression ratios, the BDCT method results in the block boundaries being visible in the reconstructed image (after decoding). This distortion is called the blocking effect or blocking artifacts. In this research we illustrate the blocking effect and its causes. Then, we propose two methods for reducing the blocking effect using a 3-mode adaptive filtering and a 3-mode adaptive interpolation. We realize the two proposed methods by two suitable algorithms, seeking to effectively and relatively simply reduce the blocking artifacts without causing degradation of the other characteristics of the image quality (taking into account some specific requirements of video coding). We present the results of applying both the algorithms. The results show the effectiveness of the two proposed methods.