This paper proposes Stochastic LIM for simulations of transmission lines with uncertainties. Such simulations are traditionally performed using sampling techniques such as Monte Carlo, which are slow to converge and often computationally expensive. Since analysis of uncertainties in electronic packaging is critical to design for reliability and performance, simulators such as Stochastic LIM can provide fast and accurate uncertainty quantification to support design objectives and shorten design cycles. To demonstrate these capabilities, we model transmission lines using equivalent circuits where the circuit parameters are random variables reflecting uncertainties in the physical structure. The solutions to the random circuits are then obtained using Stochastic LIM, and the results are compared to Monte Carlo analysis of the same circuits using traditional deterministic circuit solvers. Techniques for projection of uncertainties in the physical space into uncertainties in the equivalent circuit are discussed.