We investigate the fractal and statistical properties of underground muons recorded at 570 hg/cm2 and study their response to solar activity variations in the second part of solar cycle 21. A constant feature detected throughout the whole period considered is the self-affine nature of the underground muon fluctuations which display a scaling range extending approximately from a few hours to more than 2 months. An important result of our study is that the scaling and spectral exponents are positively correlated with the sunspot cycle. In addition, the intensity distribution shows a more marked presence of short- and long-term fluctuations near solar maximum. The presence of solar modulation in the muon record suggests dimensions of the heliosphere at least as large as a few scattering mean free paths of the 1.8-TV primaries.