Analytical solutions are presented for three problems involving transient diffusion in apparatuses with two reservoirs (case 1) or one reservoir system with either impermeable boundary (case 2) or zero concentration boundary condition (case 3). This was accomplished by using a one-dimensional multi-layer diffusion model. The proposed solutions may be useful for studying the movement of solute and gas from reservoirs into soil sample or chambers, which are commonly used for measuring the aqueous and gaseous diffusion coefficients in soil, as well as for solute or gases movement in layered soils. The behavior of the solutions is illustrated by comparing case 1 with two experimental examples showing the concentration at different locations as a function of time. For case 1 it was found that for the commonly used experimental apparatuses, the effective diffusion coefficient was related to the first eigenvalue of a transcendental equation. For all of the three cases, increasing the diffusion coefficient in reservoirs will approximate our solution to the transient diffusion in a tube with well-stirred end-bulbs of finite size very well. The error caused by using the well-stirred approximation was presented for case 2. The difference between case 2 and case 3 was also analyzed.