Abstract In this article, we prove an Omega result for the Hecke eigenvalues λ F ( n ) {\lambda_{F}(n)} of Maass forms F which are Hecke eigenforms in the space of Siegel modular forms of weight k, genus two for the Siegel modular group S p 2 ( ℤ ) {Sp_{2}({\mathbb{Z}})} . In particular, we prove λ F ( n ) = Ω ( n k - 1 exp ( c log n log log n ) ) , \lambda_{F}(n)=\Omega\biggl{(}n^{k-1}\exp\biggl{(}c\frac{\sqrt{\log n}}{\log% \log n}\biggr{)}\biggr{)}, when c > 0 {c>0} is an absolute constant. This improves the earlier result λ F ( n ) = Ω ( n k - 1 ( log n log log n ) ) \lambda_{F}(n)=\Omega\biggl{(}n^{k-1}\biggl{(}\frac{\sqrt{\log n}}{\log\log n}% \biggr{)}\biggr{)} of Das and the third author. We also show that for any n ≥ 3 {n\geq 3} , one has λ F ( n ) ≤ n k - 1 exp ( c 1 log n log log n ) , \lambda_{F}(n)\leq n^{k-1}\exp\biggl{(}c_{1}\sqrt{\frac{\log n}{\log\log n}}% \biggr{)}, where c 1 > 0 {c_{1}>0} is an absolute constant. This improves an earlier result of Pitale and Schmidt. Further, we investigate the limit points of the sequence { λ F ( n ) / n k - 1 } n ∈ ℕ {\{\lambda_{F}(n)/n^{k-1}\}_{n\in{\mathbb{N}}}} and show that it has infinitely many limit points. Finally, we show that λ F ( n ) > 0 {\lambda_{F}(n)>0} for all n, a result proved earlier by Breulmann by a different technique.