A fissured aquifer may be considered as a dense network of fissures separated by low permeability matrix blocks. A conceptual modeling of such a system consists of an infinite number of parallel fractures separated by constant width matrix slabs. While the fissures are assumed to be main flow conduits, the fluid in the porous matrix blocks are considered to be virtually immobile. The mathematical model of the transport of a solute and/or contaminant which assumes a purely convective flow in fissures and diffusion into the matrix blocks consists of two coupled differential equations. An analytical solution of this model for the case of solute entering into the system at a constant concentration has been presented by Skopp and Warrick in Soil Sci Soc Am Proc 38:545-550, 1974. Note however, Skopp and Warrick (Soil Sci Soc Am Proc 38:545-550, 1974) have not considered the additional processes of adsorption and radioactive decay. Unfortunately, their solution had computational limitations as it involved numerical integration of a quite complex expression. Therefore, one had to turn to employing numerical Laplace transform inverters to compute the solutions. This work presents simple real space analytical solutions for the contaminant transport model described above including the adsorption and radioactive decay. The real space solutions have been developed using the method of double Laplace transform and binomial series approximation. An accurate approximate solution has also been presented which converges to the exact solution only after computing three terms in the series full solution. The developed model has been used for 1) assessment of the efficiency of numerical Laplace transform algorithms and 2) investigation of the degree and scale of contamination, and 3) designing remediation schemes for the already contaminated aquifers.