diff --git a/include/ctranslate2/storage_view.h b/include/ctranslate2/storage_view.h
index 8834ef651..d25d47048 100644
--- a/include/ctranslate2/storage_view.h
+++ b/include/ctranslate2/storage_view.h
@@ -238,6 +238,9 @@ namespace ctranslate2 {
 
     friend std::ostream& operator<<(std::ostream& os, const StorageView& storage);
 
+    template <typename T>
+    void print_tensor(std::ostream& os, const T* data, const std::vector<dim_t>& shape, size_t dim, size_t offset, int indent) const;
+
   protected:
     DataType _dtype = DataType::FLOAT32;
     Device _device = Device::CPU;
diff --git a/src/storage_view.cc b/src/storage_view.cc
index 0cbdf25c2..13f973bf8 100644
--- a/src/storage_view.cc
+++ b/src/storage_view.cc
@@ -440,44 +440,77 @@ namespace ctranslate2 {
     return os;
   }
 
-  std::ostream& operator<<(std::ostream& os, const StorageView& storage) {
-    StorageView printable(storage.dtype());
-    printable.copy_from(storage);
-    TYPE_DISPATCH(
-      printable.dtype(),
-      const auto* values = printable.data<T>();
-      if (printable.size() <= PRINT_MAX_VALUES) {
-        for (dim_t i = 0; i < printable.size(); ++i) {
-          os << ' ';
-          print_value(os, values[i]);
+    std::ostream& operator<<(std::ostream& os, const StorageView& storage) {
+      // Create a printable copy of the storage
+      StorageView printable(storage.dtype());
+      printable.copy_from(storage);
+
+      // Check the data type and print accordingly
+      TYPE_DISPATCH(
+        printable.dtype(),
+        const auto* values = printable.data<T>();
+          const auto& shape = printable.shape();
+
+          // Print tensor contents based on dimensionality
+          if (shape.empty()) { // Scalar case
+            os << "Data (Scalar): " << values[0] << std::endl;
+          } else {
+            os << "Data (" << shape.size() << "D ";
+            if (shape.size() == 1)
+              os << "Vector";
+            else if (shape.size() == 2)
+              os << "Matrix";
+            else
+              os << "Tensor";
+            os << "):" << std::endl;
+            printable.print_tensor(os, values, shape, 0, 0, 0);
+            os << std::endl;
+          }
+      );
+
+      // Print metadata
+      os << "[device:" << device_to_str(storage.device(), storage.device_index())
+         << ", dtype:" << dtype_name(storage.dtype()) << ", storage viewed as ";
+      if (storage.is_scalar())
+        os << "scalar";
+      else {
+        for (dim_t i = 0; i < storage.rank(); ++i) {
+          if (i > 0)
+            os << 'x';
+          os << storage.dim(i);
         }
       }
-      else {
-        for (dim_t i = 0; i < PRINT_MAX_VALUES / 2; ++i) {
-          os << ' ';
-          print_value(os, values[i]);
+      os << ']';
+      return os;
+    }
+
+    template <typename T>
+    void StorageView::print_tensor(std::ostream& os, const T* data, const std::vector<dim_t>& shape, size_t dim, size_t offset, int indent) const {
+      std::string indentation(indent, ' ');
+
+      os << indentation << "[";
+      bool is_last_dim = (dim == shape.size() - 1);
+      for (dim_t i = 0; i < shape[dim]; ++i) {
+        if (i > 0) {
+          os << ", ";
+          if (!is_last_dim) {
+            os << "\n" << std::string(indent, ' ');
+          }
         }
-        os << " ...";
-        for (dim_t i = printable.size() - (PRINT_MAX_VALUES / 2); i < printable.size(); ++i) {
-          os << ' ';
-          print_value(os, values[i]);
+
+        if (i == PRINT_MAX_VALUES / 2) {
+          os << "...";
+          i = shape[dim] - PRINT_MAX_VALUES / 2 - 1; // Skip to the last part
+        } else {
+          if (is_last_dim) {
+            os << data[offset + i];
+          } else {
+            print_tensor(os, data, shape, dim + 1, offset + i * shape[dim + 1], indent);
+          }
         }
       }
-      os << std::endl);
-    os << "[" << device_to_str(storage.device(), storage.device_index())
-       << " " << dtype_name(storage.dtype()) << " storage viewed as ";
-    if (storage.is_scalar())
-      os << "scalar";
-    else {
-      for (dim_t i = 0; i < storage.rank(); ++i) {
-        if (i > 0)
-          os << 'x';
-        os << storage.dim(i);
-      }
+      os << "]";
     }
-    os << ']';
-    return os;
-  }
 
 #define DECLARE_IMPL(T)                                                 \
   template                                                              \