diff --git a/changelog.md b/changelog.md
index 3c84d97e..e3b414f2 100644
--- a/changelog.md
+++ b/changelog.md
@@ -6,6 +6,8 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 
 ### Changed
 
+- [PR40](https://github.com/scipopt/SCIPpp/pull/40) `Model::addSolution()`, `Model::setObjsense()`, `Model::setParam()`,
+  and `Model::solve()` are now const member functions.
 - [PR38](https://github.com/scipopt/SCIPpp/pull/38) Update to SCIP 10.0.0.
 
 ## [1.3.0] - 2025-10-08
diff --git a/include/scippp/model.hpp b/include/scippp/model.hpp
index cac360ea..5df6272c 100644
--- a/include/scippp/model.hpp
+++ b/include/scippp/model.hpp
@@ -47,7 +47,7 @@ class Model {
     //! Constraints.
     std::vector<SCIP_Cons*> m_cons {};
     //! Stores the return of the last %SCIP call when the default call wrapper is used.
-    SCIP_Retcode m_lastReturnCode;
+    mutable SCIP_Retcode m_lastReturnCode;
     //! Wrapper for every call to %SCIP's %C %API.
     std::function<void(SCIP_Retcode)> m_scipCallWrapper;
 
@@ -204,14 +204,14 @@ class Model {
      * Solve the model.
      * @since 1.0.0
      */
-    void solve();
+    void solve() const;
 
     /**
      * Set objective goal.
      * @since 1.0.0
      * @param objsense Minimize or Maximize.
      */
-    void setObjsense(Sense objsense);
+    void setObjsense(Sense objsense) const;
 
     /**
      * Returns the solution status.
@@ -270,7 +270,7 @@ class Model {
      * @param value to set the parameter to.
      */
     template <typename T, typename PT>
-    void setParam(params::Param<PT> parameter, T value)
+    void setParam(params::Param<PT> parameter, T value) const
     {
         auto ptValue { static_cast<PT>(value) };
         const auto* cName { parameter.scipName.data() };
@@ -346,6 +346,6 @@ class Model {
         bool completely = true,
         bool checkBounds = true,
         bool checkIntegrality = true,
-        bool checkLpRows = true);
+        bool checkLpRows = true) const;
 };
 }
diff --git a/source/model.cpp b/source/model.cpp
index 84117cbd..23ba905f 100644
--- a/source/model.cpp
+++ b/source/model.cpp
@@ -105,12 +105,12 @@ bool Model::isZero(SCIP_Real value) const
     return SCIPisZero(m_scip, value);
 }
 
-void Model::solve()
+void Model::solve() const
 {
     m_scipCallWrapper(SCIPsolve(m_scip));
 }
 
-void Model::setObjsense(Sense objsense)
+void Model::setObjsense(Sense objsense) const
 {
     m_scipCallWrapper(SCIPsetObjsense(m_scip, static_cast<SCIP_Objsense>(objsense)));
 }
@@ -156,7 +156,7 @@ bool Model::addSolution(
     bool completely,
     bool checkBounds,
     bool checkIntegrality,
-    bool checkLpRows)
+    bool checkLpRows) const
 {
     SCIP_Sol* sol { nullptr };
     m_scipCallWrapper(SCIPcreateSol(m_scip, &sol, nullptr));